Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose tha P(A beats B) = 0.6 P(A beats C) = 0.2 P(B beats C) = 0.4 and that the outcomes of the three matches are independent of one another. (a) What is the probability that A wins both her matches and that B beats C? (b) What is the probability that A wins both her matches? (c) What is the probability that A loses both her matches? (d) What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.)
Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose tha P(A beats B) = 0.6 P(A beats C) = 0.2 P(B beats C) = 0.4 and that the outcomes of the three matches are independent of one another. (a) What is the probability that A wins both her matches and that B beats C? (b) What is the probability that A wins both her matches? (c) What is the probability that A loses both her matches? (d) What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please do D.
![Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose that
\[ P(A \text{ beats } B) = 0.6 \]
\[ P(A \text{ beats } C) = 0.2 \]
\[ P(B \text{ beats } C) = 0.4 \]
and that the outcomes of the three matches are independent of one another.
**(a)** What is the probability that A wins both her matches and that B beats C?
[ ]
**(b)** What is the probability that A wins both her matches?
[ ]
**(c)** What is the probability that A loses both her matches?
[ ]
**(d)** What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.)
[ ]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ecdd586-d90f-4b01-9735-d33df7ee50d8%2F9c90b7c5-a74a-4435-be58-956961d449b6%2Fqvkymwl_processed.png&w=3840&q=75)
Transcribed Image Text:Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose that
\[ P(A \text{ beats } B) = 0.6 \]
\[ P(A \text{ beats } C) = 0.2 \]
\[ P(B \text{ beats } C) = 0.4 \]
and that the outcomes of the three matches are independent of one another.
**(a)** What is the probability that A wins both her matches and that B beats C?
[ ]
**(b)** What is the probability that A wins both her matches?
[ ]
**(c)** What is the probability that A loses both her matches?
[ ]
**(d)** What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.)
[ ]
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