Section 4.6 Probability
319
65. Bridge is a card game played by four players with a standard 52-card deck. All 52 cards are dealt to the
four players at the beginning of each hand. In 1963, women playing bridge in Kankakee, Illinois, discovered that after the deal, each player held the 13 cards of a single suit. What is the probability of one player
being dealt an entire suit?
66. Referring to Exercise 65, what is the probability of each of the four players being dealt an entire suit?
67. E 1 and E 2 are events from the same sample space; P(E 1 ) = 0.37, P(E 2 ) = 0.45, and P(E 1 d E 2 ) = 0.14.
a. Find the probability that E 2 does not occur.
b. Find the probability that either E 1 or E 2 occurs.
c. Find the probability that neither E 1 nor E 2 occurs.
68. An 8-letter password is automatically generated from the 26 lowercase letters of the English alphabet.
Each letter is equally likely to be used, and letters can be repeated.
a. What is the size of the sample space?
b. Find the probability that the word does not contain an “e.”
c. Find the probability that the word contains at least one “e.”
d. Find the probability that the word contains a single “e.”
e. Find the probability that the word contains both a single “h” and a single “x.”
f. Find the probability that the word contains either a single “h” or a single “x.”
69. A loaded die has the following probability distribution:
When the die is rolled, let E 1 be the event that the number rolled is odd, let E 2 be the event that the number
rolled is 3 or 6, and let E 3 be the event that the number rolled is 4 or more.
a. Find P(E 1 ).
b. Find P( 2 ).
c. Find P(E 3 ).
d. Find P(E 2 d E 3 ).
e. Find P(E 1 c E 3 ).
70. A congressional race has a Democratic, a Republican, and an Independent candidate in a district where
past voting patterns indicate that a Democrat is twice as likely to be elected as a Republican, and that a
Republican is four times as likely to be elected as an Independent.
a. Find the appropriate probability distribution.
b. What is the probability that a Democrat will be elected?
c. What is the probability that a Republican will not be elected?
71. At a certain school, 72% of the students play one or more sports. The percentage of students who play
one or more sports and who graduate is 67%. Find the probability that a student graduates given that the
student plays one or more sports.
x i
1
2
3
4
5
6
p(x i )
0.2
0.05
0.1
0.2
0.3
0.15
319
65. Bridge is a card game played by four players with a standard 52-card deck. All 52 cards are dealt to the
four players at the beginning of each hand. In 1963, women playing bridge in Kankakee, Illinois, discovered that after the deal, each player held the 13 cards of a single suit. What is the probability of one player
being dealt an entire suit?
66. Referring to Exercise 65, what is the probability of each of the four players being dealt an entire suit?
67. E 1 and E 2 are events from the same sample space; P(E 1 ) = 0.37, P(E 2 ) = 0.45, and P(E 1 d E 2 ) = 0.14.
a. Find the probability that E 2 does not occur.
b. Find the probability that either E 1 or E 2 occurs.
c. Find the probability that neither E 1 nor E 2 occurs.
68. An 8-letter password is automatically generated from the 26 lowercase letters of the English alphabet.
Each letter is equally likely to be used, and letters can be repeated.
a. What is the size of the sample space?
b. Find the probability that the word does not contain an “e.”
c. Find the probability that the word contains at least one “e.”
d. Find the probability that the word contains a single “e.”
e. Find the probability that the word contains both a single “h” and a single “x.”
f. Find the probability that the word contains either a single “h” or a single “x.”
69. A loaded die has the following probability distribution:
When the die is rolled, let E 1 be the event that the number rolled is odd, let E 2 be the event that the number
rolled is 3 or 6, and let E 3 be the event that the number rolled is 4 or more.
a. Find P(E 1 ).
b. Find P( 2 ).
c. Find P(E 3 ).
d. Find P(E 2 d E 3 ).
e. Find P(E 1 c E 3 ).
70. A congressional race has a Democratic, a Republican, and an Independent candidate in a district where
past voting patterns indicate that a Democrat is twice as likely to be elected as a Republican, and that a
Republican is four times as likely to be elected as an Independent.
a. Find the appropriate probability distribution.
b. What is the probability that a Democrat will be elected?
c. What is the probability that a Republican will not be elected?
71. At a certain school, 72% of the students play one or more sports. The percentage of students who play
one or more sports and who graduate is 67%. Find the probability that a student graduates given that the
student plays one or more sports.
x i
1
2
3
4
5
6
p(x i )
0.2
0.05
0.1
0.2
0.3
0.15