Chapter 10, Problem 9CT

To determine

Toexplain:

Is itpossible by using formula of $P\left(AandB\right)=P\left(A\right)\cdot P\left(B|A\right)$ where given events are independent.

Answer to Problem 9CT

For independent events, it is not possible to use $P\left(AandB\right)=P\left(A\right)\cdot P\left(B|A\right)$ formula for conditional probability.

Explanation of Solution

Given information:

Formula:

  $P\left(AandB\right)=P\left(A\right)\cdot P\left(B|A\right)$

Independent events: $A$ and $B$

Two events $A$ and $B$ are independent evets when one event does not affect the occurrence of another event.

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

  $P\left(AandB\right)=P\left(A\right)\cdot P\left(B\right)$

If two events $A$ and $B$ are dependent events, then probability that both occur is the product of the probability of the first event and conditional probability of the second event given the first event symbolically.

  $P\left(AandB\right)=P\left(A\right)\cdot P\left(B|A\right)$

Therefore, for independent events, it is not possible to use the formula for conditional probability.