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Q23E

Expert-verifiedFound in: Page 467

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 _{$\frac{1}{16}$}

** **

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

** **

Formula used are:

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

** **

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

$p\left(\frac{E}{F}\right)=\frac{p(E\cap F)}{P\left(F\right)}\phantom{\rule{0ex}{0ex}}=\frac{{\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}^{5}}{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\phantom{\rule{0ex}{0ex}}=\frac{1}{16}$

** **

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

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