Al Huiteen School
Mathematics Performance Task 1-Term 2(2021/2022)
Name:
Grade: 10ADV
Marks: 20
Submission Date: 17.02.2022
Determine whether the scenario involves independent or dependent events. Explain Your
Reasoning.
1. A box of chocolates contains five milk chocolates, five dark chocolates, and five white
chocolates. You randomly select and eat three chocolates. The first piece is milk
chocolate, the second is dark chocolate, and the third is white chocolate.
Dependent event, because the first event has an effect on the second event (so if I
eat a milk chocolate piece, I’m not going to but it back so then the next probability is
going to depend on the fact that by I aet a chocolate and the next probability after
that is going to depend on those two events before it, because of that it is
dependent event.
2. A bag contains eight red marbles and four blue marbles. You randomly pick a marble
and then pick a second marble without returning the marbles to the bag. The first
marble is red, and the second marble is blue. Dependent event, 8+4=12 marbles in
the bag so, if I pick a red marble the probability of picking that would be 8\12 and
we did not return that marble to the bag so then I have 11 marble in the bag and for
picking the blue marble 4\11 so these depend on each other that means that this
probability depends on whether or not I put that marble back in the bag or not, so
because I did not return this marble to the bag the second probability depends on
the first one so because of that it is dependent event .
Determine if the scenario involves mutually exclusive events: Explain Your Reasoning.
1. A magazine contains Twelve pages. You open to a random page. The page number is
eight or ten. Mutually exclusive event, p (A or B) = p(A)+p(B) = 2\12 which can be
simplified as 1\6
2. A spinner has an equal chance of landing on each of its eight numbered regions. After
spinning, it lands in region three or six. Mutually exclusive event,
Find the Probability of the following: Explain with Steps.
1. A basket contains five apples and seven peaches. You randomly select one piece of fruit
and eat it. Then you randomly select another piece of fruit. The first piece of fruit is an
apple and the second piece is a peach. 5\12 x 7\11 = 35\132 = 0.265
2. You flip a coin and then roll a fair six-sided die. The coin lands heads-up and the die
shows an even number. 1\2 x 3\6 = 3\12 = 1\4 =0.25
3. Find the probability of drawing a king or queen from a standard deck of cards. P(k or Q)
= p(k) + p(Q) = P(k or Q) = 4\52 + 4\52 , p(k or Q) = 8\52 = 2\13
4. The probability for a driver’s license applicant to pass the road test the first time is 5/6.
The probability of passing the written test on the first attempt is 9/10. The probability of
passing both test the first time is 4/5. Are the events mutually exclusive? What is the
probability of passing either test on the first attempt? Not mutually exclusive
P(R or W) = p(R) + p(w) – p(R and w) = 5\6 + 9\10 – 4\5
= 26\15 - 4\5 = 14\15
5.Find the probability of tossing two dice and either one showing a 4. So, the possible
outcomes when tossing dice (1,2,3,4,5,6) so when we will tossing two dice 6x6 = 36
possibilities. Possibility of getting number 4 is (1,3) , (2,2) , (3,1)
Favorable outcomes = 3 , total number of possibilities = 36 so, probability = number of favorable
outcomes \ total number of possibilities = 3\36 = 1\12
6. Find the probability of selecting an ace or a red card from a deck of cards. P(ace OR red)
= p(ace) + p(red) – p(ace And red)
= 4+26-2 = 28
28\52
= 7\13
7. Determine the probability that a card drawn from a deck is red or a face card.
Not mutually exclusive, P(A)= 26\52, p(B) = 12\52 p(A and B) = 6\52
P(A or B) = 26\52 + 12\52 – 6\52 = 32\52 = 8\13
8. A bag contains cards numbered from 1 to 14. One card is drawn at random. Find the
probability of:
a) selecting a prime number or a multiple of four.
b) selecting a multiple of two or a multiple of three.
c) selecting a 3 or a 4.
d) selecting an 8 or a number less than 8.
9. Events A and B are independent. Find the missing probability.
a) P(A) = / P(B) = /  P(B|A) = ?
b) P(B) = / P(A|B) = 1/ P(A) = ?
Note: Without reasoning or without steps answers will not
be accepted.