Chapter 10.7, Problem 15HP

To determine

To find: The number of times coins tossed.

Answer to Problem 15HP

The number of times coins tossed is $48$ .

Explanation of Solution

Given information: Probability of tails coming up is $\frac{9}{16}$ .

Calculation Probability of tails coming up is $\frac{9}{16}$ .

  $\begin{array}{l}P(head)+P(tail)=1\\ P(head)+\frac{9}{16}=1\\ P(head)=1-\frac{9}{16}\\ P(head)=\frac{16-9}{16}=\frac{7}{16}(i)\end{array}$

Let the coin tossed $x$ times.

Number of times heads coming up is $21$ .

  $P(head)=\frac{21}{x}(ii)$

Equation $(i)\mathrm{and}(ii)$ are probability of heads so both are equal.

  $\begin{array}{l}\frac{7}{16}=\frac{21}{x}\\ \mathrm{cross}\mathrm{multiply}\\ 7x=21\times 16\\ x=\frac{21\times 16}{7}\\ x=3\times 16=48\end{array}$

Thus, the number of times coins tossed is $48$ .