Chapter 10.3, Problem 15E

To determine

To calculate:

The error in finding the given conditional probability.

Answer to Problem 15E

The corrected answer of the conditional probability is $P\left(Yes|Tokyo\right)=0.126$ .

Explanation of Solution

Given information:

		City			Total
		Tokyo	London	Washington, D.C.
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,

  $A$ : Tokyo and yes

  $B$ : Tokyo

  $C$ : Yes|Tokyo

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:

  $\begin{array}{l}P\left(A\right)=0.049\\ P\left(B\right)=0.39\end{array}$

The condition probability was computed mistakenly and the probability of Tokyoby taking:

  $P\left(B\right)=0.356$

But the conditional probability has to be computed using the probability of Tokyo as:

  $P\left(B\right)=0.39$

The correct probability is shown as:

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

Substitute the values,

  $\begin{array}{l}P\left(C\right)=\frac{0.049}{0.39}\\ P\left(C\right)=0.126\end{array}$

The corrected answer of the conditional probability is $P\left(Yes|Tokyo\right)=0.126$ .