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PROBABILITY REVIEW
1. A spinner is divided into 4 equal regions: Red, Blue, Green, and Yellow. The spinner is spun and a regular six-sided
dice is rolled, and both results are noted as a single combined outcome.
a. Give any representation of the sample space that shows all possible combined outcomes.
b. Find the probability of spinning a
Blue OR rolling a 6.
c. Find the probability of NOT spinning
a Red AND rolling less than a 5.
1
7
9
, p  B 
, and p  A  B  
.
2
10
10
a. Find p  A  B 
2. Suppose that p  A  
b. Are events A and B mutually exclusive?
Give a reason for your answer.
c. Are events A and B independent?
Give a reason for your answer.
3. In a class of 20 students, there are 8 students who like skiing, there are 14 students who like swimming, and there
are 3 students who do NOT like skiing or swimming.
a. Draw a diagram that represents this
situation.
b. Find the probability that a randomly
selected student likes BOTH skiing
and swimming.
c. Find the probability that a randomly
selected student likes skiing, given
that he/she does NOT like swimming.
d. If two students are randomly selected
from the class, find the probability that
exactly ONE of them likes skiing.
4. What can you conclude if X and Y are mutually exclusive and independent events? Explain.
5. Zena is running in two track events: the 100 meter sprint (event A), followed by the 200 meter sprint (event B). She
has a 42% chance of winning the 100 meter sprint. If she wins the 100 meter sprint, then she has a 71% chance of
winning the 200 meter sprint. If she loses the 100 meter sprint, then she has a 33% chance of winning the 200
meter sprint.
a. Draw a diagram that represents this
situation.
b. Find the probability of Zena winning the
200 meter sprint.
c. Are the events of winning the 100 meter
sprint and the 200 meter sprint independent
or dependent? Explain your answer.
d. Find the probability that Zena won the
100 meter sprint, given that she wins the
200 meter sprint.
6. Ruby has a 0.671 chance of hitting a target each time that she takes a shot. Ruby shoots four times. Find the
probability that Ruby:
a. hits the target with all four shots
b. hits the target with at least one of her shots
b. misses the target with her last two shots, given that she hits it with her first two shots
7. A and B are 2 events such that p  A  0.3 and p  B   0.5 and p  A  B   0.55 . Calculate the probabilities of
the following events:
a.
p  A B
b.
pB A
8. A bag contains 16 marbles, 7 of which are red and the remaining 9 are white. On Quang’s first selection, he selects a
marble, records its color, and places it BACK IN THE BAG along with TWO OTHER MARBLES OF THE SAME COLOR.
Quang then selects a marble and records its color.
a. Draw a tree diagram to show the sample
space of outcomes and its probabilities.
the same color.
b. Find the probability that the two
marbles that Quang selected are
9. Tim travels to ISM by bus 5 days a week, from Monday to Friday. The probability that he catches the 06:00 a.m. bus
on Monday is 0.35. The probability that he catches the 06:00 a.m. bus on any other day is 0.75. A weekday is chosen
at random.
a. Are the events (day of the week and catching the bus) dependent or independent? Explain how you know.
b. Find the probability that Tim catches
the 06:00 a.m. bus on a randomly
chosen weekday.
c. Given that Tim catches the 06:00 a.m.
bus on a randomly chosen weekday,
find the probability that the chosen
weekday is a Monday.
10. Alex scores on 85% of his free throws, while Bill scores on 75% of his free throws. Determine the probabilities of the
following events:
a. Alex misses his next free throw AND
Bill scores on at least 1 of his next
4 free throws.
b. Alex scores on exactly 2 of his next
3 free throws OR Bill misses exactly
1 of his next 2 free throws.
11. Eight different books are to be placed on a shelf. Three of the books are about science. How many arrangements
are possible if:
(a) there are no restrictions
(b) the science books are always placed together
(c) there has to be a science book at each end of the shelf?
12. A company randomly selects 10 contest winners from a pool of 327 entrants. Given that 153 entrants were male
and 174 entrants were female,
(a) Find the probability that no men are selected as winners.
(b) Find the probability that 5 men and 5 women are selected as winners.