Chapter 8.3, Problem 8.53E

(a)

To determine

To calculate the probability that all seven people have type O blood.

Answer to Problem 8.53E

  $0.0032$

Explanation of Solution

Binomial theorem:

  $P(X=k)=C{}_k\times p^k\times {(1-p)}^{n-k}$

  $\begin{array}{l}n=7,k=7\\ p=0.44\end{array}$

  $\begin{array}{l}$ P(X=7)=C{}_7\times {(0.44)}^7\times {(1-0.44)}^{7-7}$$ ={(0.44)}^7$=0.0032\\ =0.32\%\end{array}$

(b)

To determine

To calculate the probability that exactly four of those selected have type O blood.

Answer to Problem 8.53E

  $0.2304$

Explanation of Solution

Binomial theorem:

  $P(X=k)=C{}_k\times p^k\times {(1-p)}^{n-k}$

  $\begin{array}{l}n=7,k=4\\ p=0.44\end{array}$

  $\begin{array}{l}$ P(X=4)=C{}_4\times {(0.44)}^4\times {(1-0.44)}^{7-4}$$ =35\times {(0.44)}^4\times {(0.56)}^3$=0.2304\\ =23.04\%\end{array}$