Chapter 10.3, Problem 6Q

To determine

To find: the missing probability.

Answer to Problem 6Q

The missing probabilityis: 0.2.

Explanation of Solution

Given:

  $\begin{array}{l}P\left(A\right)=0.25\\ P\left(A\text{ and }B\right)=0.05\end{array}$

Calculation:

Two events A and B are independent events if and only if the probability that both events occur is the product of the probabilities of the events. Symbolically,

  $P\left(A\text{ and }B\right)=P\left(A\right)\cdot P\left(B\right)\dots \left(1\right)$

From information given,

  $P\left(A\right)=0.25,P\left(A\text{ and }B\right)=0.05$

Substitute the values in rule (1). Therefore, probability of B is as follows:

  $\begin{array}{l}P\left(A\text{ and }B\right)=P\left(A\right)\cdot P\left(B\right)\\ \to 0.05=0.25\cdot P\left(B\right)\\ \to P\left(B\right)=\frac{0.05}{0.25}\\ =0.2\end{array}$

Conclusion:

Therefore, the the missing probability is: 0.2.