PROBABILITY PRACTICE PROBLEMS
1. A pair of dice is thrown. If the two numbers appearing are different,
find the probability that the sum is six.
Ans. 2/15
2. A pair of dice is thrown. Find the probability that the sum is 10 or
greater if a 5 appears on at least one of the dice.
Ans. 3/11
3. Suppose that five good fuses and two defective ones have been mixed up.
To find the defective fuses, we test them one-by-one, at random and without
replacement. What is the probability that we are lucky and find both
defective fuses in the first two tests?
Ans. 1/21
4. A class contains 10 men and 20 women of which half the men and half the
women have brown eyes. Find the probability that the person chosen at random
is a man or has brown eyes.
Ans. 2/3
5. If the sample probabilities are respectively, 0.09, 0.15, 0.21, and 0.23
that a person purchasing a new automobile will choose green, white, red, or
blue, what is the probability that a given buyer will purchase a new
automobile in one of those colors?
Ans. 0.68
6. Box A contains 8 items of which 3 are defective, and box B contains 5
items of which 2 are defective. An item is drawn at random from each box.
What is the probability that both items are non-defective?
Ans. 3/8
7. In a poker hand consisting of 5 cards, find the probability of holding 4
hearts and 1 club.
Ans. 0.3576%
8. The probability that a man will live 10 more years is ¼ and the probability
that his wife will live 10 more years is 1/3. Find the probability that at
least one will be alive in 10 years.
Ans. ½
9. The probability that a construction generator will operate satisfactorily
for 5 years is 0.80 and that a welding machine will operate satisfactorily
over the same period is 0.75. Find the probabilities that in a 5-year period
both generators and welding machine operate satisfactorily.
Ans. 0.60
10. You have an equally likely chance of choosing any integer from 1 to 20.
Find the probability that a prime number is chosen.
Ans. 8/20
11. A box contains 15 billiard balls, which are numbered 1 to 15. A ball is
drawn at random and the number is written down. Determine the following
probabilities that the number is even and less than 5.
Ans. 2/15
12. A pair of dice is tossed. Find the probability of getting a total of 8
Ans. 5/36
13. Two cards are drawn in succession from a deck without replacement. What
is the probability that both cards are greater than 2 and less than 8?
Ans. 95/663
14. In a high school graduating class of 100 students, 54 studied
mathematics, 69 studied history, and 35 studied both mathematics and history.
If one of these students is selected at random, find the probability that
a. the student took mathematics or history ; Ans. 88/100 or 22/25
b. the student did not take either of these subjects; Ans. 12/100 or 3/25
c.the student took history but not mathematics; Ans. 34/100 or 17/50
15. Five cards are drawn from a standard 52-deck card deck. What is the
probability that the first two cards are red?
Ans. 0.245
16. A classroom contains 71 students. 10 of them are Chinese, 24 are Japanese
and 37 Filipinos. If three students are randomly asked to get out of the
room, one after the other, what is the probability that all 3 students are
Chinese?
Ans. 0.0021