Probability Probability (worded) 1 Tara rolls a fair 6­sided dice once. a circle the word below that best describes the probability of Tara getting a number less than 6 Impossible unlikely evens likely certain b On the probability scale below, mark with a cross (x) the probability that Tara gets a 10 c On the probability scale below, mark with a letter 'F' the probability that Tara gets 5 d Yasmin rolls a fair 6­sided dice once. She then throws a fair coin once. List all the possible combinations Yasmin can get. 2 Meela has a 6­sided spinner. The sides of the spinner are numbered 2, 2, 2, 3, 3, 5 a from the following list, choose the word that best describes the likelihood that the spinner will land on 2. impossible unlikely evens likely certain b On the probability scale, mark with a cross (x), the probability of getting 3. c On the probability scale, mark with letter 'F', the probability of getting 5. 3 Valentina is going to have a meal. She can choose one starter and one main course from the menu. Menu Starter Main course Soup Beef Prawn Tuna Mushrooms Vegetarian Write down all the possible combinations Valentina can choose. 1 Probability Probability 1 There are 8 pencils in a pencil case. 1 pencil is red. 4 pencils are blue The rest are black. A pencil is taken at random from the pencil case. Write down the probability that the pencil is black. 2 Sue has a bag of 18 sweets. 5 of the sweets are blue 7 of the sweets are red 6 of the sweets are green Sue takes at random a sweet from the bag. Write down the probability that sue a takes a red sweet b does not take a green sweet c takes a yellow sweet. 3 There are only red counters, blue counters and green counters in a bag. There are 5 red counters, There are 6 blue counters, There are 1 green counter. Jim takes at random a counter from the bag. a Work out the probability that Jim takes a counter that is not red. Jim puts the counter back in the bag. He then puts some green counters in the bag. 1 The probability of taking at random a red counter is now 3 . b Work out the number of green counters that are now in the bag. 2 Probability Probability 1 Jane rolls a dice 120 times. Here are the results of her experiment. Number 1 2 3 4 5 6 Frequency 19 18 23 22 21 17 a work out the probability of rolling a 6 on Jane's dice b Work out the probability of rolling 5 or more on Jane's dice. 2 Lorna carries out a survey about the number of times customers go to a shop. She asks at random 100 customers how many times they went to the shop last month. The table shows Lorna's results. Number of times 0 1 2 3 4 5 6 more then 6 Frequency 4 12 13 17 25 13 11 5 One of the 100 customers is chosen at random. a What is the probability that this customer went to the shop 5 or more times? Last month the shop had a total of 1500 customers. b Work out an estimate for the number of customers who went to the shop exactly 2 times last month. 3 The probability that a biased dice will land on a three is 0.4 Paul is going to roll the dice 200 times. Work out an estimate for the number of times the dice will land on a three. 3 Probability 4 Jack sows 300 wildflower seeds. The probability of a seed flowering is 0.7 Work out an estimate for the number of seeds that will flower. 5 The probability that a biased dice will land on a four is 0.2. Pam is going to roll the dice 200 times. Work out an estimate for the number of times the dice will land on 4. 6 Angel Ltd manufacture components for washing machines. The probability that a component will fit the washing machine is 0.995. Angel LTD manufacture 10 000 components each day. Work out an estimate for the number of components that will not fit the machine each day. 7 Martin bought a packet of mixed flower seeds. The seeds produce flowers that are red or blue or white or yellow. The probability of a flower seed producing a flower of a particular colour is: Colour Probability Red 0.6 Blue 0.15 White 0.15 Yellow a Write down the most common colour of a flower. Martin chooses a flower seed at random from the packet. b Work out the probability produced will be Yellow. c Write down the probability that the flower produced will be orange. 4 Probability 8 Here is a 4­sided spinner. The sides are labelled red, blue, yellow and green. The spinner is biased. The probability that the spinner will land on each of the colours is shown in the table. Colour probability Red 0.45 Blue 0.3 Yellow x Green 0.1 Jo spins the spinner once. a Work out the probability, x, that the spinner will land on yellow. Daniel spins the spinner 500 times. b Work out an estimate for the number of times the spinner will land on blue. 9 Riki has a packet of flower seeds. The table shows each of the probabilities that a seed taken at random will grow into a flower that is pink or red or blue or yellow. Colour Probability pink 0.15 red 0.25 blue 0.20 yellow 0.16 white a Work out the probability that a seed taken at random will grow into a white flower. There are 300 seeds in the packet. All the seeds grow into flowers. b Work out an estimate for the number of red flowers. 10 A bag contains some balls which are red or blue or green or black. Yvonne is going to take one ball at random from the bag. The table shows each of the probabilities that Yvonne will take a red ball or a blue ball or a black ball. Colour Probability Red 0.3 Blue 0.17 Green Black 0.24 Work out the probability that Yvonne will take a green ball. 5 Probability 11 A bag contains only red, green and blue counters. The table shows the probability that a counter chosen at random from the bag will be red or will be a green. Colour Probability Red 0.5 Green 0.3 Blue Mary takes a counter at random from the bag. a Work out the probability that Mary takes a blue counter. The bag contains 50 counters. b Work out how many green counters there are in the bag. 12 The table shows the probability that a counter taken at random from the bag will be red or blue. Colour Probability red 0.2 blue 0.6 white black The number of white counters in the bag is three times as the black counters in the bag. Tania takes at random a counter from the bag. a Work out the probability that Tania takes a white counter. There are 240 counters in the bag. b Work out the number of red counters in the bag. 6 Probability Tree diagrams 1 Amy and Beth are going to take a driving test tomorrow. The probability Amy will pass the test is 0.7 The probability Beth will pass the test is 0.8 Use the probability tree diagram top work out the probability a both women will pass the test Amy b only Amy will pass the test c neither woman will pass the test. Beth 0.8 Pass Pass 0.7 Not pass Pass Not pass Not pass 2 Mumtaz and Barry are going for an interview. The probability that Mumtaz will arrive early is 0.7 The probability that Barry will arrive early is 0.4 the two events are independent. Mumtaz a Complete the probability tree diagram. 0.7 b Work out the probability that Mumtaz and Barry will both arrive early. Barry 0.4 Early Early Not early Not early Early Not early c Work out the probability that just one person will arrive early. 7 Probability 3 A bag contains 9 coloured discs. 3 of the discs are red and 6 of the discs are black. Asif is going to take two discs at random from the bag, with the replacement. a Complete the tree diagram. b Work out the probability that Asif will take two black discs. 1st c Work out the probability that Asif takes two discs of the same colour. 2nd Red Red Black Red Black Black 4 There are only red marbles and green marbles in a bag. There are 5 red marbles and 3 green marbles. Dwayne takes at random a marble from the bag. He does put the marble back in the bag. Dwayne takes at random a second marble from the bag. a Complete the tree diagram. 1st Marble 2nd Marble Red Red Green Red Green Green b Work out the probability that Dwayne takes marbles of different coloures. 8 Probability 5 The probability that it will rain on Monday is 0.6 When it rains on Monday, the probability that it will rain on Tuesday is 0.8 When it does not rain on Monday, the probability that it will rain on Tuesday is 0.5 Monday Tuesday Rains Rains Not rains Rains Not rains Not rains a Complete the probability tree diagram. b Work out the probability that it will rain on both Monday and Tuesday. 6 Martin and Luke are students in the same maths lesson. The probability that Martin will bring a calculator to a lesson is 0.8 The probability that Luke will bring a calculator to a lesson is 0.6 a Complete the probability tree diagram. Martin Luke Calculator Calculator No calculator Calculator No calculator No calculator b Work out the probability that both Martin and Luke will not bring a calculator to a maths lesson. 9 Probability Exercise 1 Simon and Asha take a motorcycle test. The probability that Simon will pass is 0.9 The probability that Asha will pass is 0.8 a Complete the probability tree diagram. b Work out the probability that both will fail the test. Simon Asha Pass Pass Fail Pass c Work out the probability that exactly one of them will pass the test. Fail Fail 2 Samina has a round pencil case and a square pencil case. There are 4 blue pens and 3 red pens in the round pencil case. There are 3 blue pens and 5 red pens in the square pencil case. Samina takes at random one pen out of each pencil case. a Complete the probability tree diagram. Round pencil case Square pencil case blue blue red blue red red b Work out the probability that the pens Samina takes atre both red. 3 Jill is going to play one game of tennis and one game of badminton. The probability that she will win the game of tennis is 1 4 The probability that she will win the game of badminton is 2 5 a Complete the probability tree diagram. Tennis Badminton win win lose win lose lose b Work out the probability that Jill wins only Tennis game. 10 Probability Frequency tree 1 Fred owns 80 books. He has not read 15 of these books. 20 of the books he has read are hardbacks. He has 52 paperbacks in total. The rest of the books are hardbacks. a Use this information to complete this frequency tree. Paperback has read 80 hardback paperback has not read hardback b Fred chooses one of his books at random. Work out the probability that it is a paperback he has not read. 2 60 people each took a driving test. 21 of these people were women. 18 of these 60 people failed their test. 27 of the men passed their test. a Use this information to complete the frequency tree. passed women failed 60 passed men b One of the men is chosen at random. Work out the probability that this man failed his test. failed 3 120 adults were asked if they voted in the general election. 58 of these adults were male. 7 of the females did not vote. 103 of the adults voted. vote a Complete the frequency tree. male did not vote vote female b One of the males is chosen at random. Work out the probability that this male did not vote. did not vote 11 Probability Conditional Probability 1 A bag contains 10 coloured discs. 4 of the discs are red and 6 of the discs are black. Asif is going to take two discs at random from the bag, without the replacement. a Complete the tree diagram. b Work out the probability that Asif will take two black discs. c work out the probability that Asif takes two discs of different colours. 1st 2nd Red Red Black Red Black Black 2 There are only red marbles and green marbles in a bag. There are 5 red marbles and 3 green marbles. Dwayne takes at random a marble from the bag. He does not put the marble back in the bag. Dwayne takes at random a second marble from the bag. a Complete the tree diagram. 1st Marble 2nd Marble Red Red Green Red Green Green b Work out the probability that Dwayne takes marbles of different coloures. 12 Probability 3 Julie has 10 tulip bulbs in a bag. 7 of the tulip bulbs will grow into red tulips. 3 of the tulip bulbs will grow into yellow tulips. Julie takes at random two tulip bulbs from the bag. She plants the bulbs. a Complete the tree diagram 1st bulb 2nd bulb red red yellow red yellow yellow b Work out the probability that at least one of the bulbs will grow into yellow tulip. 4 There are 10 socks in a drawer. 7 of the socks are brown. 3 of the socks are gray. Beth takes at random two socks from the drawer without the replacement. a Complete the tree diagram. 1st sock 2nd sock Brown Brown Grey Brown Grey Grey b Work out the probability that Beth takes two sock of the same colour. 13 Probability 5 A box of chocolates contains 10 milk chocolates and 12 plain chocolates. Two chocolates are taken at random without replacement. Work out the probability thatboth chocolates will be milk chocolates 6 Max and Lili have 9 bottles of juice in their fridge. They have: 4 bottles of orange juice 3 bottles of cranberry juice 2 bottles of mango juice They each take a bottle at random from the fridge. What is the probability that they each take a bottle of the same type of juice? 7 Carol has 20 biscuits in a tin. She has 12 plain biscuits 5 chocolate biscuits 3 ginger biscuits Carolyn takes at random two biscuits from the tin. Work out the probability that the two biscuits were not the same type. 8 There are 5 red pens, 3 blue pens and 2 green pens in a box. Gary takes at random a pen from the box and gives the pen to his friend. Gary then takes at random another pen from the box. Work out the probability that both pens are the same colour. 14 Probability 9 Here are seven tiles. 1 1 2 2 2 3 3 Jim takes at random a tile. He does not replace the tile. Jim then takes at random a second tile. a Calculate the probability that both the tiles Jim takes have the number 1 on them b Calculate the probability that the number on the second tile Jim takes is greater than the number on the first tile he takes. 10 Here are 8 cards. There ia a number on each card. 2 3 3 4 4 6 6 6 Erin puts the 8 cards in a bag. She takes at random a card from the bag and does not replace it. Erin then takes at random a second card from the bag. Calculate the probability that the number on the second card is double the number on the first card. 15
