Book edition 7th

Author(s) Kenneth H. Rosen

Pages 808 pages

ISBN 9780073383095

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Short Answer

Question 23. To determine
What is the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up heads?

The conditional probability is _{$\frac{1}{16}$}

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

A coin is flipped five times and the first flip is heads.

Step 2. Definition and formula to be used

Formula used are:

$p (\frac{E}{F}) = \frac{p (E \cap F)}{P (F)}$

Step 3. Compute probability

Exactly heads will appear out of the flips if and only if the remaining flips all come up heads. The probability of this is ${(\frac{1}{2})}^{4} = \frac{1}{16}$

One can also compute the answer by labelling the event that the first coin flip comes up tails.

Then the probability that a total of heads will appear given that the first flip came up tails is

$p (\frac{E}{F}) = \frac{p (E \cap F)}{P (F)} = \frac{{(\frac{1}{2})}^{5}}{\frac{1}{2}} = \frac{1}{16}$

The conditional probability is $\frac{1}{16}$ .

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Discrete Mathematics and its Applications

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Short Answer

Question 23. To determine
What is the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up heads?

Step by Step Solution

Step 1. Given information

Step 2. Definition and formula to be used

Step 3. Compute probability

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Discrete Mathematics and its Applications

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Short Answer

Question 23. To determine What is the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up heads?

Step by Step Solution

Step 1. Given information

Step 2. Definition and formula to be used

Step 3. Compute probability

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Question 23. To determine
What is the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up heads?