Chapter 10.3, Problem 21E

To determine

To explain: whether the decisions of friend is correct or not

Answer to Problem 21E

Here, the probability to reach goal is greatest when Routine B is used. So, the routine should be B and the friend is correct.

Explanation of Solution

Given:

  

Calculation:

Use the findings to make a two-way table that shows joints and marginal relative frequencies. There are a total of $25$ observations in the table:-

Results
	Reached goal	Does not reach goal	Total
Routine A	$\frac{5}{25}=0.20$	$\frac{3}{25}=0.12$	$\frac{8}{25}=0.32$
Routine B	$\frac{4}{25}=0.16$	$\frac{2}{25}=0.08$	$\frac{6}{25}=0.24$
Routine C	$\frac{7}{25}=0.28$	$\frac{4}{25}=0.16$	$\frac{11}{25}=0.44$
Total	$\frac{16}{25}=0.64$	$\frac{9}{25}=0.36$	$1$

Find conditional probability by dividing each joint relative frequency in the “reach goal” column by the marginal relative frequency in its corresponding row.

  $\begin{array}{l}P\left(reachgoal|routineA\right)=\frac{P\left(routineAandreachgoal\right)}{P\left(routineA\right)}\\ \text{ =}\frac{\frac{5}{25}}{\frac{8}{25}}\\ \text{ =0}\text{.62}\\ P\left(reachgoal|routineB\right)=\frac{P\left(routineBandreachgoal\right)}{P\left(routineB\right)}\\ \text{ =}\frac{\frac{4}{25}}{\frac{6}{25}}\\ \text{ =0}\text{.66}\\ P\left(reachgoal|routineC\right)=\frac{P\left(routineCandreachgoal\right)}{P\left(routineC\right)}\\ \text{ =}\frac{\frac{7}{25}}{\frac{11}{25}}\\ \text{ =0}\text{.63}\end{array}$

Based on the sample, the probability that goal reached is greatest when Routine B is used. Therefore, the routine should be B.

Conclusion:

Therefore, the probability to reach goal is greatest when Routine B is used. So, the routine should be B and the friend is correct.