Homework Problems for Basic Probability Laws
1.
A person is randomly selected from a group of Farmers and Engineers.
Let E be the event "an Engineer is chosen" and F be the event "a Farmer is chosen".
Describe the following using words.
2.
A card is randomly drawn from a standard deck of playing cards.
Find the following probabilities:
A = the card is black
B = the card is higher than a ten
C = the card is a heart
A) 
D) 
3.
A card is randomly drawn from a standard deck of playing cards.
Find the following probabilities:
A = the card is a club
B = the card is black
C = the card is {2, 3, 4}
4.
Find the following probabilities if:
The probability event A occurs is .2
The probability event B occurs is .4
The probability event A and B occurs is .15
A) A does not occur
B) B does not occur
C) A or B occurs
D) neither A nor B occurs
5. Let A, B and C be mutually exclusive events.
Find the following probabilities if:
The probability event A occurs is .26.
The probability event B occurs is .38.
The probability event C occurs is .21.
A) event A does not occur
B) event B does not occur
C) event C does not occur
D) events A and C occur
E) event A does not occur and event B does not occur and event C does not occur
F) all three events occur
Determine if the following events are mutually exclusive events.
A pair of fair dice are rolled.
6. The sum of the two dice is 2, 4, 7 and the sum is 3, 5, 8
7. The sum of the dice is 5 and the sum of the dice is 2
8. One die is a 5 and the sum of the dice is 7
9. An even number occurs and the sum is 7
12.
In San Luis Obispo the probability of reading the Telegram Tribune is .82. The probability of reading the Easy Ad is .62.
The probability of reading both papers is .12.
Find the probability of not reading the Telegram Tribune and not reading the Easy Ad.
13. A fair coin is flipped three times. Find the probability that it will come up tails at most twice?
14. Five random letters of the alphabet are arranged. A letter may be used more than once. What is the probability that at least one letter is an A, E, I, O or U?
15. At a certain hotel, customers are offered valet parking. If four men checked their cars in with the valet, and the cars are returned at random, what is the probability that at least one man receives the wrong car?
16.
Two cards are drawn from a standard deck of playing cards.
What is the probability that at least one of the cards is a face card?
(Do this problem two ways: first work this problem without use of the compliment, and then use the compliment.)
17.
Three cards are drawn from a standard deck playing cards.
What is the probability that at least one is a 2, 3, 5 or 6?
(Do this problem two ways: first work this problem without use of the compliment, and then use the compliment.)
18. A certain jar consists of eight green marbles and four black. If two marbles are drawn at random, find the probability that both marbles are the same color.
19.
A certain box contains candy sticks; three grape, five cherry. If four candies are chosen at random, what is the probability that:
A) at least two will be cherry sticks?
B) no more than one will be grape sticks?
20. A committee consists of four men and six women. If a committee of three is chosen at random, what is the probability that:
A) none are women.
B) the majority of the committee are women.
Homework Solutions
1A. An Engineer is NOT chosen. (A Farmer is chosen)
1B. A Farmer is NOT chosen. (An Engineer is chosen)
1C. An Engineer and Farmer are chosen.
1D. An Engineer or Farmer is chosen.
2. .69, 0, .85, .23, .08
3. .23, .42, .88, .25, .38
4. .8, .6, .45, .55
5. .74, .62, .79, 0, .36, 0
6. ME
7. ME
8. Not ME
9. Not ME
10. Not ME
11. ME
12. .32
13. .88
14. .66
15. .96
16. .41
17. .68
18. .52
19. .93, .5
20. .03, .67