Some review problems, binomial probabilities and quiz questions with solutions.

1. The probability that Tony will move to Winnipeg is 2/9, and the probability that
he will marry Angelina if he moves to Winnipeg is 9/20. The probability that he
will marry Angelina if he does not move to Winnipeg is 1/20. Draw a tree
diagram to show all outcomes.
1. What is the probability that Tony will move to Winnipeg and marry
Angelina?
To be continued ...

2. The probability that Tony will move to Winnipeg is 2/9, and the probability that
he will marry Angelina if he moves to Winnipeg is 9/20. The probability that he
will marry Angelina if he does not move to Winnipeg is 1/20. Draw a tree
diagram to show all outcomes.
2. What is the probability that Tony does not move to Winnipeg but does
marry Angelina?

3. The probability that Tony will move to Winnipeg is 2/9, and the probability that
he will marry Angelina if he moves to Winnipeg is 9/20. The probability that he
will marry Angelina if he does not move to Winnipeg is 1/20. Draw a tree
diagram to show all outcomes.
3. What is the probability that Tony does not move to Winnipeg and
does not marry Angelina?

4. One card is drawn at random from a deck of 52 cards. What is the probability
of drawing an ace or a diamond?

5. In a Pre-Cal 40S class of 25 students, seven students say they like Dr.
Pepper, 11 students like Diet Dr. Pepper, and 3 like both. What is the
probability that a student will not like either Dr. Pepper or Diet Dr.
Pepper?

6. A rack contains 15 dresses. Five of the dresses are blue, six are green,
and 4 are yellow. If selling each of the dresses is equally likely, what is
the probability that if six dresses are sold, exactly two will be green?

7. In a car lot, 25% of the inventory are SUV’s, and 75% are passenger
cars. 80% of the SUV’s, and 65% of the passenger cars, have air
conditioning. What is the probability that a chosen vehicle will be an
SUV given the vehicle has air conditioning?

8. A box of eight razor blades contains two defective blades. If two blades
are drawn at random, with the first not replaced, what is the probability
that exactly one of the two blades will be defective?

9. Mixed Practice ...
(a) How many different 4 digit numbers are there in which all the
digits are different?
(b) If one of these numbers is randomly selected, what is the probability it
is odd?
(c) What is the probability it is divisable by 5?

10. The probability of hitting a target when throwing a dart is 5/7. If 6 darts are
thrown, what is the probability of exactly 4 hits?

11. If a biased coin is tossed 6 times, what is the probability of obtaining exactly 3
heads if the probability of getting heads on any one toss is 2/5?

12. There are 10 tickets in a hat, numbered from 1 to 10. If two tickets are drawn,
what is the probability that the sum of the numbers on the tickets will be odd?

14. A shootout consists of teams A and B taking alternate shots on goal. The first
team to score wins. Team A has a probability of 0.3 of scoring with any one
shot. Team B has a probability of 0.4 of scoring with any one shot. If Team A
shoots first, what is the probability of Team A winning on its third shot?

15. In room 1 there are 12 boys and 8 girls. In room 2 there are 7 boys and 9 girls.
If a student is selected at random from one of the rooms, what is the
probability that the student is a girl?

16. It is known that 10% of a population has a certain disease. A blood test for the
disease gives a correct diagnosis 95% of the time. The test is equally reliable
for persons with or without the disease. What is the probability that a person
whose blood test shows positive for the disease actually has the disease?