2. Roll a fair die. Let A = an odd number is rolled, B = a 3 is rolled. Find:
a. P(A)
b. P(not A)
c. P(A and B)
d. P(A or B)
3. From a deck of 52 cards, a card is selected at random
Let A = the event the card chosen is a heart
Let B = the event the card chosen is a face card
Let C = the event the card chosen is an ace
Let D = the event the card chosen is an 8
Let E = the event the card chosen is a 10 or a Jack
Tell if the following sets of events are mutually exclusive.
a. A,B
b. C,E
c. B, E
d. B,C,D
e. A,C,D,E
4. Toss a fair coin, let A=H, let B=T; find P(A or B)
5. Pick a card from a standard 52 card deck. Let A = Ace is picked, let B = Diamond is picked; find P(A or B)
6. 12 socks are in a box. 6 red, 1 white, 3 blue, and 2 green. If 1 sock is picked from the box at random, determine the probability
a. the sock is blue.
b. the sock is blue or red.
c. the sock is not white.
7. As reported by D & B in Business Failure Record the number of commercial failures for the year 1990 by type of industry are as follows.
Let A = event it was in wholesale trade, B = event it was in retail trade, and T = event it was in either wholesale trade or retail trade,
and suppose a failed business is selected at random.
a. Use the table and the f/N rule to find P(T)
b. Express event T in terms of A and B
c. Determine P(A)
d. Determine P(B)
e. Compute P(T) using the special addition rule and your results from parts b-d.
8. As reported by the U.S. Bureau of Justice, approximately 56.5% of jail inmates are white, 94% are male and 53.5% are white males. Suppose
a jail inmate is selected at random. Let W = the event the inmate chosen is white M = the event the inmate chosen is male
a. Find P(W)
b. Find P(M)
c. Find P(W & M)
d. Determine P(W or M)
e. Obtain the probability that a randomly selected inmate is female
9. Consider the experiment of selecting one card at random from a deck of 52 playing cards. Find the probability the card selected is:
a. either a spade or a face card.
b. Either a spade or a face card or a even numbered card.
10. The following contingency table compares grades between Males and Females on a Stats Test.
a. How many cells does the table have?
b. How many females made A’s?
c. Find P(Female|A)
d. Find P(A|Female)
11. There are 50 students in a class, 30 are female and 20 are male. If 2 students are selected at random without replacement, give the
probability you choose
a. a male and a female
b. 2 males
c. 2 females
If 2 students are selected at random with replacement, give the probability you choose
d. a male and a female
e. 2 males f. 2 females
12. Cards numbered 1,2,3,...10 are placed in a box. The box is shaken and a blindfolded person selects two successive cards
without replacement.
a. What is the probability that the first card selected in numbered 6?
b. Given that the first card selected is numbered 6, what is the probability the second card is numbered 9?
c. What is the probability of selecting first a 6 and then a 9?
d. What is the probability that both cards selected are numbered over 5?
13. In a deck of 52 cards, let
A = the event a face card is selected
B = the event a king is selected
C = the event a heart is selected
a. Is B independent of A?
b. Is B independent of C?