Chapter 10.6, Problem 22E

To determine

To explain:

The comparison of probability value of $5$ speakers system and $3$ speaker system

Answer to Problem 22E

For any values of $p$ , a $5$ speaker is more likely to functions that $3$ speaker system.

Explanation of Solution

Whether the speaker is functioning or not, can use the binomial distribution for the value of $p$ a $5$ speaker is more likely to functions that $3$ speaker system.

For the $3$ speakers, $C{}_3{\left(0.5\right)}^3{\left(0.5\right)}^{n-3}$ is the expression at least $50\%$ of the speaker is functioning property.

Same as for the $5$ speakers, $C{}_5{\left(0.5\right)}^5{\left(0.5\right)}^{n-5}$ is the expression at least $50\%$ of the speaker is functioning property.

Hence, for any values of $p$ , a $5$ speaker is more likely to functions that $3$ speaker system.