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8. Suppose a coin is flipped four times. Let A be the event that the first and last flips result in opposite faces, and let B be the event that exactly two heads appear in the sequence of tosses. You may assume that each of the sixteen head/tail sequences have the same probability. (a) Find P(An B). P(Aºn B) (b) Find P(An Bº). (as a fraction in lowest terms); (as a numerical approximation)

8. Suppose a coin is flipped four times. Let A be the event that the first and last flips result in opposite faces, and let B be the event that exactly two heads appear in the sequence of tosses. You may assume that each of the sixteen head/tail sequences have the same probability. (a) Find P(An B). P(Aºn B) (b) Find P(An Bº). (as a fraction in lowest terms); (as a numerical approximation)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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8. Suppose a coin is flipped four times. Let A be the event that the first and last flips result in opposite faces, and let B be the event that exactly two heads appear in the sequence of tosses. You may assume that each of the sixteen head/tail sequences have the same probability. (a) Find P(An B). P(Aºn B) (b) Find P(An Bº). P(An B) = (as a fraction in lowest terms); P(BA) (as a numerical approximation) (as a fraction in lowest terms); (as a numerical approximation) 9. Suppose a fair coin is tossed seven times. Let A be the event that a prime number of heads is observed, and B be the event that at least six tosses came up heads. Compute P(BA). (Careful! The number 2 is a prime number.) (as a fraction in lowest terms); (as a numerical approximation) 8
Transcribed Image Text:8. Suppose a coin is flipped four times. Let A be the event that the first and last flips result in opposite faces, and let B be the event that exactly two heads appear in the sequence of tosses. You may assume that each of the sixteen head/tail sequences have the same probability. (a) Find P(An B). P(Aºn B) (b) Find P(An Bº). P(An B) = (as a fraction in lowest terms); P(BA) (as a numerical approximation) (as a fraction in lowest terms); (as a numerical approximation) 9. Suppose a fair coin is tossed seven times. Let A be the event that a prime number of heads is observed, and B be the event that at least six tosses came up heads. Compute P(BA). (Careful! The number 2 is a prime number.) (as a fraction in lowest terms); (as a numerical approximation) 8
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