Chapter 10.4, Problem 17E

To determine

Tocalculate:

The probability that a randomly selected person would buy the fruit drink.

Answer to Problem 17E

The probability that a randomly selected person would buy the fruit drink is $0.4742$ .

Explanation of Solution

Given information:

Male focus group $=45\%$

Responses of buying focus milk of males $=40\%$

Responses of buying focus milk of females $=54\%$

Calculation:

Assume that event $A$ denote maleand event $B$ denote fruit drink.

Then, with the help of given information given probability as follows:

  $P\left(A\right)=0.47,P\left(\overline{A}\right)=0.53,P\left(B|A\right)=0.40,P\left(B|\overline{A}\right)=0.54$

So, need to find the $P\left(\overline{B}\right)$

Then, the required probability is as follows:

  $\begin{array}{l}P\left(\overline{B}\right)=P\left(AandB\right)+P\left(\overline{A}andB\right)\\ =P\left(A\right)\cdot P\left(B|A\right)+P\left(\overline{A}\right)\cdot P\left(B|\overline{A}\right)\\ =\left(0.47\right)\left(0.40\right)+\left(0.53\right)\left(0.54\right)\\ =0.4742\end{array}$

Hence, the answer is $0.4742$ .

So, the probability that a randomly selected person would buy the fruit drink is $0.4742$ .