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Expert-verified Found in: Page 353 ### The Practice of Statistics for AP

Book edition 4th
Author(s) David Moore,Daren Starnes,Dan Yates
Pages 809 pages
ISBN 9781319113339 # Toss $4$ times Suppose you toss a fair coin $4$ times. Let $X=$ the number of heads you get. (a) Find the probability distribution of$X$. (b) Make a histogram of the probability distribution. Describe what you see. (c) Find $P\left(X\le 3\right)$ and interpret the result.

(a)Probability distribution of $X$ is (b) (c) $P\left(X\le 3\right)=93.75%$

See the step by step solution

## Part (a) Step 1: Given information

Given in the question that , you toss a fair coin$4$ times. Let $X$ = the number of heads you get

We need to find the probability distribution of $X$.

## Part (a) Step 2: Explanation

If $H$ is heads and $T$ is tails, there are $16$ different ways to throw the fair coin four times:

Each of these outcomes has an equal chance of occurring$\frac{1}{16}$.

The product of the number of related outcomes and the probability yields the probability distribution of $X=$ "the number of heads": $x$ $0$ $1$ $2$ $3$ $4$ $P\left(X=x\right)$ $\frac{1}{6}$ $\frac{4}{16}$ $\frac{6}{16}$ $\frac{4}{16}$ $\frac{1}{16}$

## Part (b) Step 3: Given information

Given in the question that , you toss a fair coin 4 times. Let X = the number of heads you get

We need to make a histogram of the probability distribution.

## Step 4: Explanation(part b)

Consider the given table: Each bar's width must be equal, and its height must be equal to the probability: The histogram is around 2 degrees symmetric.

## Part (c) Step 1: Given information

Given in the question that, you toss a fair coin $4$ times. Let $X$ = the number of heads you get.

We need to find $P\left(X\le 3\right)$.

## Part (c) Step 2: Explanation

Consider the given table: $P\left(X\le 3\right)=P\left(X=0\right)+P\left(X=1\right)+P\left(X=2\right)+P\left(X=3\right)\phantom{\rule{0ex}{0ex}}=\frac{1}{16}+\frac{4}{16}+\frac{6}{16}+\frac{4}{16}\phantom{\rule{0ex}{0ex}}=0.9375$

We should expect to get $3$ heard or less in around $93.75$ or $94$ of the $100$ times we perform the quadruple toss of the coin. ### Want to see more solutions like these? 