Chapter 13.5, Problem 1CFU

To determine

To explain:The relationship between conditional probability and the probability of two independent events.

Answer to Problem 1CFU

When two events A and B are independent events then conditional probability is $P\left(A|B\right)=P\left(A\right)$ .

Explanation of Solution

Given information:

The terminologies conditional probability and the probability of two independent events.

Consider the terminologies conditional probability and the probability of two independent events.

Probability of an event Eis $P\left(\text{E}\right)=\frac{\text{number of outcome}}{\text{total number of outcome}}$ .

Consider two events A and Bsuch that they are independent events. Then $P\left(A\text{ and B}\right)=P\left(A\right)\cdot P\left(B\right)$ .

Given an event B , the conditional probability of event A is $P\left(A|B\right)=\frac{P\left(A\text{ and B}\right)}{P\left(B\right)}$ where $P\left(B\right)\ne 0$ .

If thereare conditional events, then conditional probability it,

  $\begin{array}{c}P\left(A|B\right)=\frac{P\left(A\text{ and B}\right)}{P\left(B\right)}\\ =\frac{P\left(A\right)\cdot P\left(B\right)}{P\left(B\right)}\\ =P\left(A\right)\end{array}$

Thus, when two events A and B are independent events then conditional probability is $P\left(A|B\right)=P\left(A\right)$ .