Chapter 5.3, Problem 91E

To determine

To find: that at least 1 of them is a universal donor.

Answer to Problem 91E

  $P\left(\text{at least one }O\right)=52.63\%$

Explanation of Solution

Given:

As person with O-negative blood are universal donors, 7.2% of American population have O-negative blood.

Concept used:

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

Complement rule: $P\left(\text{not}A\right)=1-P\left(A\right)$

Calculation:

  $P\left(\text{O}\right)=7.2\%=0.072$

Complement rule:

  $P\left(\text{not}A\right)=1-P\left(A\right)$

Apply complement rule to find the probability of not having type O:

  $\begin{array}{l}P\left(\text{not}O\right)=1-P\left(O\right)\\ =1-0.072=0928\end{array}$

Multiplication rule:

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

Apply multiplication rule to find the probability of 10 people not having type O:

  $\begin{array}{l}P\left(10\text{ not }O\right)={\left(P\left(\text{not }O\right)\right)}^{10}\\ ={\left(0.928\right)}^{10}\approx 0.4737\end{array}$

Use the complement rule to obtain the probability of obtaining at least one person with type O:

  $\begin{array}{l}P\left(\text{at least one }O\right)=1-P\left(\text{10not }O\right)\\ =1-0.4737\\ =0.5263=52.63\%\end{array}$