Download 8-10 Probability Practice Test

Name_________________________________
Date: ____________
Lesson 8-10: Unit 8: Probability Practice Test
Learning Goals:
What types of questions can we expect on the Probability test?
Key Terms
In words
Complementary Events
Mutually Exclusive
Not Mutually Exclusive
Conditional Probability
Independence
In symbols
1) If P(passing the Mathematical Studies exam) = 0.95, find P(not passing the Mathematical Studies).
[1 mark]
2) An urn contains 10 red, 6 green and 3 blue marbles. Ron chooses three marbles from the urn.
Assume that Ron does not replace the marbles and find each probability.
i. Ron chooses all three red marbles.
[2 marks]
ii. Ron chooses three red or three blue marbles
[2 marks]
3) Which of the following numbers cannot be the probability of some event? Explain your reasoning for
each.
[2 marks]
0.71
4.1
4) If P (A)  2 and
5
P (B ) 
2 , find P (A  B )
3
1
8
- 0.5
if A and B are independent.
1.21
[2 marks]
5) Given 𝑃(𝐴 ∪ 𝐵) = 0.82, 𝑃(𝐴) = 0.45 𝑎𝑛𝑑 𝑃(𝐵) = 0.57.
a. Find 𝑃(𝐴 ∩ 𝐵)
[2 marks]
b. Find P(B|A)
[2 marks]
c. Find P(A|B)
[2 marks]
d. Are events A and B mutually exclusive? Justify your answer with math.
[2 marks]
e. Are events A and B independent? Justify your answer with math.
[2 marks]
6) The probability that you will solve any given math problems correctly is 0.80. Find the probability
that you will solve 3 randomly selected math problems correctly.
[2 marks]
7) Given P( A  B) 
1
3
and P ( B )  find P(A|B).
3
5
[2 marks]
8) The data in the table below refers to a sample of 60 randomly chosen plants.
a. Find the probability of a plant being in a shady environment.
[1 mark]
b. Find the probability of a plant having a low growth rate and being in a dark environment.
[1 mark]
c. Find the probability of a plant not being in a dark environment.
[1 mark]
d. Find the probability that a plant has a high growth rate, given that it is in a shady environment.
[1 mark]
e. Given that a plant is in a dark environment, find the probability that it has a low growth rate.
[1 mark]
9) The probability, p, that James gets up before 07.00 is 0.95.
If James gets up before 07.00, the probability, t, that he arrives at school on time is 0.98.
If James gets up later than 07.00, the probability that he arrives at school on time is 0.55.
(a) Complete the tree diagram
[3 marks]
(b) Calculate the probability that James gets up before 07.00 and is on time for school. [1 mark]
(c) Calculate the probability that James does not arrive at school on time.
[1 mark]
(d) Given that James does not arrive to school on time, find the probability that he gets up before
7:00.
[2 marks]
10)
Consider the Venn diagram below showing the probabilities of events A and B.
a. Find each probability
i. P(A)
[1 mark]
ii. P(B)
[1 mark]
iii. P(A ∪ 𝐵)
[2 marks]
iv. 𝑃(𝐴|𝐵)
[2 marks]
b. Are events A and B independent? Why or Why not? (Use the test to check!)
[2 marks]
11) A box contains 10 coloured light bulbs, 5 green, 3 red and 2 yellow. One light bulb is selected at
random and put into the light fitting of room A.
(a)
What is the probability that the light bulb selected is
(i)
green?
[1 mark]
(ii)
not green?
[1 mark]
A second light bulb is selected at random and put into the light fitting in room B.
(b)
What is the probability that
(i)
the second light bulb is green given the first light bulb was green?
[1 mark]
(ii)
both light bulbs are not green?
[2 marks]
(iii) one room has a green light bulb and the other room does not have a green light
bulb?
[3 marks]
A third light bulb is selected at random and put in the light fitting of room C.
(c)
What is the probability that all three rooms have green light bulbs?
[2 marks]