IB1 Math SL
SA 7D.v2 Test: Probability
Name________________________
Baier
Francis
Martin-Bauer
Show all work to receive full marks. Unless otherwise stated, all numerical answers should be
given exactly or correct to three significant figures.
1. [Maximum mark: 7]
Let A and B be independent events, where P(A)  0.3 and P(B)  0.6 .
(a) Find P(AB) .
[2]
(b) Find P(AB) .
[2]
(c) (i) On the following Venn diagram, shade the region that represents A  B’ .
(ii) Find P(AB) .
[3]
2. [Maximum mark: 10]
Sue wishes to hire a taxicab from a company which has a large number of taxicabs. The taxicabs are
randomly assigned by the company.
The probability that a taxicab is yellow is 0.4.
The probability that a taxicab is a Fiat is 0.3.
The probability that a taxicab is yellow or a Fiat is 0.6.
(a) Find the probability that the taxicab hired by Sue is not a yellow Fiat.
[6]
(b) Draw a labelled Venn diagram to represent the problem. Include the probabilities of each region in
the diagram.
[4]
3. [Maximum mark: 15]
At a large school, students are required to learn at least one language, Spanish or French. It is known that
75% of the students learn Spanish, and 40% learn French.
(a) Find the percentage of students who learn both Spanish and French.
[2 marks]
(b) Find the percentage of students who learn Spanish, but not French.
[2 marks]
At this school, 52 % of the students are girls, and 85 % of the girls learn Spanish.
(c) A student is chosen at random. Let G be the event that the student is a girl, and let S be the
event that the student learns Spanish.
(i)
Find P(G∩S) .
(ii) Show that G and S are not independent.
[5 marks]
(d) A boy is chosen at random. Find the probability that he learns Spanish.
[6 marks]
4. [Maximum mark: 14]
Adam travels to school by car (C ) or by bicycle (B). On any particular day he is equally likely to travel by
car or by bicycle. The probability of being late (L) for school is 1/6 if he travels by car. The probability of
being late for school is 1/3 if he travels by bicycle. This information is represented by the following tree
diagram.
(a) Complete the following tree diagram.
[3]
L
1/6
C
___
1/2
1/3
___
L’
L
B
___
L’
(b) Find the probability that Adam will travel by car and be late for school.
[2]
(c) Find the probability that Adam will be late for school.
[4]
(d) Given that Adam is late for school, find the probability that he travelled by car.
[3]
Adam will go to school three times next week.
(e) Find the probability that Adam will be on time every day.
[2]
5. [Maximum mark: 6]
The following table shows the probability distribution of a discrete random variable X .
x
0
2
5
9
P(X = x)
0.3
k
4k
0.2
(a) Find the value of k .
[3 marks]
(b) Find E(X) .
[3 marks]
6. [Maximum mark: 8]
The probability of obtaining “tails” when a biased coin is tossed is 0.57. The coin is tossed ten times.
(a) Find the probability of obtaining at least four tails;
[4 marks]
(b) Given that there are at least 4 tails, fine the probability that there are at most 5 tails.
[4 marks]
(c) If the coin is flipped 500 times, how many times would you expect to get tails?
[2 marks]
Academic Honesty Pledge
Please re-write the following statement in your handwriting in the space provided below and endorse with a
signature.
“On my honor, I have neither given nor received any aid on this examination.”
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