Chapter 13, Problem 13.18CYS

To determine

To find: The probability that you win on none of your plays, if you play three times.

Answer to Problem 13.18CYS

Option (a): The probability that you win on none of your plays is 0.94.

Explanation of Solution

Reason for the correct option:

It is given that the probability of winning any one play is 0.02. The probability that you win on none of your plays is,

$\begin{array}{c}P\left(\text{None}\right)=\left(1-0.02\right)\left(1-0.02\right)\left(1-0.02\right)\\ ={\left(1-0.02\right)}^3\\ =0.94\end{array}$

Thus, probability that you win on none of your plays is 0.94.

Reason for the incorrect answers:

Option (b) and option (c) are incorrect, because the corresponding probability is not obtained from the formula of the independence of events.

Conclusion:

Therefore, option (a) is correct.

Statistics Concept Introduction

Introduction:

Independent events:

Two events are said to be independent events if the occurrence of one event does not affect the occurrence of another event. If events A and B are independent then,

$P\left(A\cap B\right)=P\left(A\right)P\left(B\right)$