Chapter PIV, Problem 20RE

(a)

To determine

To find: the probability that a smoker is not one of the first four students interviewed.

Answer to Problem 20RE

0.2401

Explanation of Solution

The chance that a high school student would smoke is 0.30

The chance that a smoker is not one of the first 4 students’ interviews is

  $\begin{array}{c}P\left(X=0\right)=\left(0.7\right)\left(0.7\right)\left(0.7\right)\left(0.7\right)\\ =0.2401\end{array}$

There is a 24.01% probability that none of the first four students that are interviewing is a smoker.

(b)

To determine

To find: the chance that the sixth person to select is the first smoker.

Answer to Problem 20RE

0.0504

Explanation of Solution

Let X be the number of interviews with students to determine the first smoker.

  $\begin{array}{c}P\left(X=6\right)={\left(0.7\right)}^5\left(0.3\right)\\ =0.0504\end{array}$

There is a 5% probability that the 6th person will be the first smoker you interview.

(c)

To determine

To Find: the chance of selecting no more than 2 smokers out of 10 people.

Answer to Problem 20RE

0.38

Explanation of Solution

Formula used:

  $P\left(X=r\right)=C{}_x{\left(p\right)}^x{\left(1-p\right)}^{n-x}$

Calculation:

Let X be the number of tobacco-smoking students.

The total amount of students is 10.

X is binom (10, 0.3)

  $\begin{array}{c}P\left(X\le 2\right)={\displaystyle \sum _{x=0}^{2}C{}_x{\left(0.3\right)}^x{\left(0.7\right)}^{n-x}}\\ =0.38\end{array}$

There is a 38% risk of no more than 2 students smoking.