Chapter 11.2, Problem 19E

(a)

To determine

To explain:

The conclusion for following statement using histogram:

  $27$ heads observed on flipping a coin for $50$ times

Answer to Problem 19E

The company claims about $27$ heads is correct as the probability value for the event is close to the mean of the histogram.

Explanation of Solution

Given information:

  

  $\begin{array}{l}n\left(E\right)=27\\ n\left(S\right)=50\end{array}$

Formula used:

Probability of an event is given by the following expression:

  $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$

Where,

  $n\left(E\right)$ : Number of ways it can happen

  $n\left(S\right)$ : Total number of outcomes

Calculation:

On flipping a coin for $50$ times, $27$ heads observed. Now, probability of getting $27$ heads is calculated as below:

  $\begin{array}{l}P\left(27\right)=\frac{27}{50}\\ P\left(27\right)=0.54\end{array}$

Here, $P\left(27\right)=0.54$ is close to the mean of the histogram $0.50$ . So, the company claims about $27$ heads is true.

(b)

To determine

To explain:

The conclusion for following statement using histogram:

  $33$ heads observed on flipping a coin for $50$ times

Answer to Problem 19E

The company claims about $33$ heads is incorrect as the probability value for the event is close enough to the mean of the histogram.

Explanation of Solution

Given information:

  

  $\begin{array}{l}n\left(E\right)=33\\ n\left(S\right)=50\end{array}$

Formula used:

Probability of an event is given by the following expression:

  $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$

Where,

  $n\left(E\right)$ : Number of ways it can happen

  $n\left(S\right)$ : Total number of outcomes

Calculation:

On flipping a coin for $50$ times, $33$ heads observed. Now, probability of getting $33$ heads is calculated as below:

  $\begin{array}{l}P\left(33\right)=\frac{33}{50}\\ P\left(33\right)=0.66\end{array}$

Here, $P\left(33\right)=0.66$ is not close to the mean of the histogram $0.50$ . So, the company claims about $33$ heads is not true.