Chapter 13.6, Problem 23HP

To determine

The probability of the coin tossed.

Answer to Problem 23HP

The coin was tossed $48$ times

Explanation of Solution

The probability of choosing tails in an experiment is $\frac{9}{16}$

As know that in the coin experiment

  $P\left(\text{heads}\right)+P\left(\text{tails}\right)=1$

So the probability of choosing heads in this experiment

  $\begin{array}{l}P\left(\text{heads}\right)+P\left(\text{tails}\right)=1\\ P\left(\text{heads}\right)+\frac{9}{16}=1\\ P\left(\text{heads}\right)=1-\left(\frac{9}{16}\right)\text{or}P\left(\text{heads}\right)=\frac{7}{16}\end{array}$

To find the no. of coins tossed, use the formula.

  $\text{P}\left(\text{heads}\right)\text{×No}\text{.}\text{of}\text{times}\text{a}\text{coin}\text{has}\text{been}\text{tossed}\left(\text{X}\right)\text{=No}\text{.}\text{of}\text{heads}\text{obatined}$

So,

  $\begin{array}{l}\frac{7}{16}\times X=21\\ 7.X=21\times 16\\ 7X=336\\ X=48\text{times}.\end{array}$

Conclusion:

Hence, the coin was tossed $48$ times.