Concept explainers
a
Find the probability that the person wears 2 blue socks.
a
Answer to Problem 24E
The probability that the person wears 2 blue socks is 0.0909.
Explanation of Solution
There are 4 blue, 5 gray, and 3 black socks.
The total number of socks is 12, and there are 4 blue socks.
The probability of selecting a blue sock from the 12 socks is
Thus, the probability of wearing two blue socks is as follows:
The probability that theperson wears 2 blue socks is 0.0909.
b.
Find the probability that the person wears no gray socks.
b.
Answer to Problem 24E
The probability that theperson wears no gray socks is 0.3182.
Explanation of Solution
There are 4 blue, 5 gray, and 3 black socks.
The total number of socks is 12, and there are 5 gray socks. The remaining 7 socks are not gray.
The probability of not selecting a gray sock from the 7 socks is
Thus, the probability of not wearing gray socks is as follows:
The probability that theperson wears no gray socks is 0.3182.
c.
Find the probability that the person wears at least one black sock.
c.
Answer to Problem 24E
The probability that theperson wears at least one black sockis 0.4545.
Explanation of Solution
There are 4 blue, 5 gray, and 3 black socks.
The total number of socks is 12, and there are 3 black socks. The remaining 9 socks are not black.
The probability of not selecting a black sock from the 9 socks is
Thus, the probability of wearing at least one black sock is as follows:
The probability that theperson wears at least one black sock is 0.4545.
d.
Find the probability that the person wears a green sock.
d.
Answer to Problem 24E
The probability that theperson wears a green sock is 0.
Explanation of Solution
There are 4 blue, 5 gray, and 3 black socks.
Here, there are no green socks.
Thus, the probability that theperson wears a green sock is 0.
e.
Find the probability that the person wears matching socks.
e.
Answer to Problem 24E
The probability that theperson wears matching socks is 0.2879.
Explanation of Solution
Matching blue socks:
There are 4 blue, 5 gray, and 3 black socks.
From Part (a), the probability of wearing matching blue socks is 0.0909.
Matching gray socks:
The total number of socks is 12, and there are 5 gray socks.
The probability of selecting a gray sock from the 12 socks is
Thus, the probability of wearing two gray socks is as follows:
The probability of wearing matching gray socks is 0.1515.
Matching black socks:
The total number of socks is 12, and there are 3 black socks.
The probability of selecting a black sock from the 12 socks is
Thus, the probability of wearing two black socks is as follows:
The probability of wearing matching black socks is 0.0455.
The probability of obtaining matching socks is calculated using the addition rule of disjoint events as follows:
The probability that theperson wears matching socks is 0.2879.
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Chapter 3 Solutions
OPENINTRO:STATISTICS
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning