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IB-MYP Mathematics Year 10 Unit Test: Probability PART A Name: . . . . . . . . . . . . . Grade: A: . . . . . Time: 50 mins C: . . . . . Criteria A, level 1 – 2 1. A card is drawn from a pack of 52 cards. What is the probability the card drawn is: (a) a diamond? (b) a two? 2. Two dice are rolled. What is the probability that: (a) the first die shows a 5 (b) the second die also shows a 5? 3. Write the following probabilities as odds: 1 (a) 7 4. Write the following odds as probabilities: (a) 5–1 (b) 2–5 (b) 4 . 7 (c) 3–4 5. State the event that is complementary to each of the following: (a) it is raining tomorrow (b) drawing a King from a deck of cards Criteria A, level 3 - 4 6. The weather bureau forecasts the chance of rain for the next day as 65%. What is the probability of it not raining the next day? 7. A bag contains 40 balls of which 22 are red, 9 are blue and the rest black. Find: (a) Pr (not green) (b) Pr (neither blue nor black). 8. 170 Year 10 students are surveyed on how much they like two bands. 105 students like Coldplay and 135 students like Rhiannon. 85 students like both subjects. (a) Draw a Venn Diagram to show this (b) What is the probability that a student selected at random likes: i. Coldplay ii. Coldplay only (c) neither Coldplay nor Rhiannon? 9. A set of cards is numbered {1, 2, 3, 4 … 48, 49, 50}. A card is selected at random. Find: (a) Pr (not an odd number) (b) Pr (not a multiple of 3). (c) Pr (multiple of 4 or a multiple of 5) (d) Pr(a number less than 20 or greater than 35). 10. A raffle has 800 tickets. Mikey, Cathan and Ehan purchased 180 tickets all together. What is the probability that none of them wins? 11. A card is selected at random from a pack of 52 cards. Find: (a) Pr ( a black card or a spade) (b) Pr ( a queen or a king or a red card) . Criteria A, level 5 – 6 12. A 3-way spinner is spun 3 times in a row. Each colour has an equal chance: a. draw a tree diagram to show the sample space for 3 spins. b. What is the probability of getting green twice? c. What is the likelihood of getting yellow then 2 purples? 13. The spinner in Q12 is spun and a die is rolled. What is the probability of yellow on the spinner and 4 on the die? 14. A darts player can hit the bullseye 4 times out of every 10 throws. What is the probability of her throwing 3 bullseyes from the next 3 throws? 15. A box contains 100 iPods of which 4 are broken. Two iPods are selected. What is the probability of selecting: (a) 2 broken iPods (b) 1 good and 1 broken (c) A good iPod and then a iPod? broken iPod? 16. Two cards are randomly selected from a pack of cards. What is the probability both cards are: (a) Kings (b) Less than 10 in value 17. Using correct notation, describe these areas in the Venn Diagram: a. A or B b. C c. B but not C or A 18. 76 students were asked which was their favourite subject – Science, English or Math. 22 chose Math 19 chose Science 3 chose Science only 12 chose Science 5 liked all three and Math 4 liked English and 32 chose English Math a. Use this information to complete the diagram below: b. Find 𝑃(𝑀𝑎𝑡ℎ ∪ 𝑆𝑐𝑖𝑒𝑛𝑐𝑒) c.. Find 𝑃(𝐸𝑛𝑔𝑙𝑖𝑠ℎ ∩ 𝑆𝑐𝑖𝑒𝑛𝑐𝑒 ∩ 𝑀𝑎𝑡ℎ′ ) IB-MYP Mathematics – Year 10 Name: . . . . . . . . . . . . . Unit Test: Probability PART B – Time: 25 mins 19. Using the information from Q18, find: a. The probability of student liking Science, given that they like Math b. The probability of a student liking English, given that they don’t like Science 20. Cathan rolls a die 200 times. a. How many times should he expect to roll a 6? b. In fact he rolls a six 28 times. Why is this, and when will he get the expected outcome? ............................................................... ............................ ........................................................................................... ............................................................... ............................ ............................................................... ............................ 21. Mr Woods and his wife, Sam, visit the City of Dreams in Macau. In Roulette, about half the numbers are red and the other half black (with one green number). They watch the games for a long time and notice that black numbers aren’t coming up. In the next game, Mr Woods bets on black. Sam bets on red. a. Give a subjective reason for each bet, and identify any errors in their approach: ............................................................. .............................. ............................................................... ............................ .................................................................... ....................... ........................................................................................... b. Given the known probabilities, why do people gamble at Casinos? ........................................................................................... ............................................................... ............................ ............................................................... ............................ ...................................................................................... ..... Do this question last! 22. Five coins are tossed at once. What is the probability of getting 3 Tails and 2 Heads?