Chapter 13.10, Problem 8PPS

To determine

The probability of tails and a number less than or equal to $5$ is to be estimated.

Answer to Problem 8PPS

The probability is $\frac{5}{12}$ .

Explanation of Solution

Given:

  

Concept Used:

Probability of an event is calculated as:

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

Where,

The probability of an event: $P$

The number of favourable outcomes: $n\left(E\right)$

The total number of events in the sample space: $n\left(S\right)$

Calculation:

Know that:

The penny has two outcomes such as tail and head. And the spun has six parts numbered on $1-6$

In the spun there are five numbers which are less than or equal to five.

The probability of tails is calculated as:

  $\begin{array}{l}P\left(A\right)=\frac{n\left(T\right)}{n\left(S\right)}\\ P\left(A\right)=\frac{1}{2}\end{array}$

The probability of a number less than or equal to $5$ is calculated as:

  $\begin{array}{l}P\left(B\right)=\frac{n\left(\le 5\right)}{n\left(S\right)}\\ P\left(B\right)=\frac{5}{6}\end{array}$

So, the probability of tails and number less than or equal to $5$ is given as:

  $\begin{array}{l}P=P\left(A\right)\times P\left(B\right)\\ P=\frac{1}{2}\times \frac{5}{6}\\ P=\frac{5}{12}\end{array}$

Conclusion:

Hence, the probability of tails and number less than or equal to $5$ is $P=\frac{5}{12}$ .