Chapter 10.3, Problem 16E

To determine

To calculate:

The error in finding the given conditional probability

Answer to Problem 16E

The corrected answer of the conditional probability is $P\left(C\right)=0.174$ .

Explanation of Solution

Given information:

		City
		Tokyo	London	Washington, D.C.	Total
Response	Yes	$0.049$	$0.136$	$0.171$	$0.356$
	No	$0.341$	$0.112$	$0.191$	$0.644$
	Total	$0.39$	$0.248$	$0.362$	$1$

  

Formula used:

Conditional probability is given by the following expression:

  $P\left(C\right)=\frac{P\left(A\right)}{P\left(B\right)}$

Where,

  $A$ : London and No

  $B$ : No

  $C$ : London

Calculation:

This question deals with study of two way table with provided the values of experiment is being considered.

This data provided and used for calculation of probability are:

  $\begin{array}{l}P\left(A\right)=0.112\\ P\left(B\right)=0.644\end{array}$

The condition probability was computed mistakenly and the probability of no has to be used instead:

  $P\left(C\right)=0.248$

The correct probability is shown as:

  $\begin{array}{l}P\left(C\right)=\frac{P\left(A\right)}{P\left(B\right)}\\ P\left(C\right)=\frac{0.112}{0.644}\\ P\left(C\right)=0.174\end{array}$

The corrected answer of the conditional probability is $P\left(C\right)=0.174$ .