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Expert-verified Found in: Page 467 ### Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095 # 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 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:

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

## 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 ${\left(\frac{1}{2}\right)}^{4}=\frac{1}{16}$

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

The conditional probability is $\frac{1}{16}$. ### Want to see more solutions like these? 