Chapter 5, Problem R5.8RE

To determine

To find: the probability of randomly selecting 10 adults and at least 1 person who believes that finding and picking up a penny is good luck.

Answer to Problem R5.8RE

0.98177 = 98.177%

Explanation of Solution

Given:

Suppose

A= adult believes that finding and picking up a penny is good luck

B= at least 1 of 10 adults believe that finding and picking up a penny is good luck

  $\overline{A}$ =One adult believes that finding and picking up a penny is good luck

  $\overline{B}$ =none of the 10 adults believe that finding and picking up a penny is good luck

  $\begin{array}{c}P\left(A\right)=33\%\\ =0.33\end{array}$

Formula used:

Multiplication Rule:

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

Complement Rule:

  $P\left(\overline{A}\right)=1-P\left(A\right)$

Calculation:

Using the complement rule:

  $\begin{array}{c}P\left(\overline{A}\right)=1-P\left(A\right)\\ =1-0.33\\ =0.67\end{array}$

Although the shipments are arbitrary chosen, it is good to assume that the shipment are independent of each other and therefore using the multiplication rule

  $\begin{array}{c}P\left(\overline{B}\right)=P\left(\overline{A}\right)\times P\left(\overline{A}\right)\times \mathrm{...}P\left(\overline{A}\right)\left(10times\right)\\ ={\left(0.67\right)}^{10}\\ =0.01823\end{array}$

Using the complement rule:

  $\begin{array}{c}P\left(B\right)=1-P\left(\overline{B}\right)\\ =1-0.01823\\ =0.98177\\ =98.177\%\end{array}$