A box contains two fair coins, two coins that are weighted so that the probability of heads is .75 and the probability of heads is .25, and one trick coin which has tails on both sides. (a) What is the probability that a randomly selected coin from the box will come up heads when flipped? (b) Suppose you randomly pick a coin from the box and flip it, and it comes up tails. What is the probability that it's the trick coin? (c) Let X be the random variable that represents the number of heads when every coin in the box is flipped. What is the probability distribution of X? (Hint: you can try counting all the outcomes, or you can remember that coin flips are independent of each other.) (d) What is the expected number of heads when all the coins are flipped?
A box contains two fair coins, two coins that are weighted so that the probability of heads is .75 and the probability of heads is .25, and one trick coin which has tails on both sides. (a) What is the probability that a randomly selected coin from the box will come up heads when flipped? (b) Suppose you randomly pick a coin from the box and flip it, and it comes up tails. What is the probability that it's the trick coin? (c) Let X be the random variable that represents the number of heads when every coin in the box is flipped. What is the probability distribution of X? (Hint: you can try counting all the outcomes, or you can remember that coin flips are independent of each other.) (d) What is the expected number of heads when all the coins are flipped?
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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Transcribed Image Text:A box contains two fair coins, two coins that are weighted so that the probability of heads is .75 and the
probability of heads is .25, and one trick coin which has tails on both sides.
(a) What is the probability that a randomly selected coin from the box will come up heads when
flipped?
(b) Suppose you randomly pick a coin from the box and flip it, and it comes up tails. What is the
probability that it's the trick coin?
(c) Let X be the random variable that represents the number of heads when every coin in the box is
flipped. What is the probability distribution of X? (Hint: you can try counting all the outcomes,
or you can remember that coin flips are independent of each other.)
(d) What is the expected number of heads when all the coins are flipped?
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