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Q.1

Expert-verifiedFound in: Page 353

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 $P(X\le 3)$ and interpret the result.

(a)Probability distribution of $X$ is

(b)

(c) $P(X\le 3)=93.75\%$

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 $X$.

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":

$x$ | $0$ | $1$ | $2$ | $3$ | $4$ |

$P(X=x)$ | $\frac{1}{6}$ | $\frac{4}{16}$ | $\frac{6}{16}$ | $\frac{4}{16}$ | $\frac{1}{16}$ |

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.

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.

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

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

Consider the given table:

Let's add the corresponding probabilities

$P(X\le 3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)\phantom{\rule{0ex}{0ex}}=\frac{1}{16}+\frac{4}{16}+\frac{6}{16}+\frac{4}{16}\phantom{\rule{0ex}{0ex}}=0.9375$

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.

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