More Probability review.

1. Last Chance Probability Review
CHANCE by flickr user eisenrah

2. The probability of a randomly chosen car being defective is 1/3. Four
(4) cars are chosen randomly in order. Given that at least two (2) cars
are defective, what is the probability that the first car is defective?

3. The probability of a randomly chosen car being defective is 1/3. Four
(4) cars are chosen randomly in order. Given that at least two (2) cars
are defective, what is the probability that the first car is defective?

5. Susan sees her friend, Tim, at his locker with a worried look on his
face. She asks, “What’s wrong?” Tim has to open his locker and
change clothes within the next five minutes. However, he has
forgotten the combination to his new lock (60 numbers). He knows that
the lock requires three different numbers. He also remembers that all
of the numbers are odd, and all of the numbers are divisible by seven.
It takes 10 seconds to dial a locker combination and 1.5 minutes to
change clothes. Is Tim likely to be ready for gym class on time?
Support your answer mathematically.

6. Two jars contain red and green marbles. Jar I contains 3 red and
2 green marbles. Jar II contains 4 red and 3 green marbles. A jar
is picked at random and two marbles are picked out of that jar in
order. If it is known that the first marble is red, what is the
probability of the second marble being red?

7. Three identical boxes each contain two drawers. In one box, each
drawer contains a gold coin. In another box, each drawer contains a
silver coin. The remaining box has a silver coin in one drawer and a
gold coin in the other. One drawer is opened and a gold coin is found.
What is the probability that the other drawer in that box also contains
a gold coin? Michael claims that the probability is 1/3. Jessica
claims it is 1/2. Raymond says the probability is 2/3.
Explain how each person may have arrived at their answer.
Who is correct? Justify your answer.

9. 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.
(a) What is the probability that Tony will move to Winnipeg and marry
Angelina?
(b) What is the probability that Tony does not move to Winnipeg but does
marry Angelina?
(c) What is the probability that Tony does not move to Winnipeg and
does not marry Angelina?

10. 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?

11. 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?

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

13. (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?

14. 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?

15. 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?

16. 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?

17. 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?

18. 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?