Question

77. Blood types Refer to Exercise 75. How surprising would it be to get more than $4$ adults with type $O$ blood in the sample? Calculate an appropriate probability to support your answer.

Short answer

The probability is greater than $5\%$, it is not unlikely to obtain more than $4$adults with blood type$○$is $P(x>4)=0.1402=14.02\%$and so the result is not surprising.

Step-by-step solution

Concept introduction

The proportion of the number of outcomes in a total group of similarly probable effects that supply a particular event to the complete number of potential products is known as probability in statistics.

Explanation

Given:
$n=7$
$p=0.44$
Let's use the Binomial Probability:
$\mathrm{P}(\mathrm{X}=\mathrm{k})=\left(\begin{array}{c}n\\ k\end{array}\right)\times p^k\times (1-p{)}^{n-k}$

$\mathrm{P}(\mathrm{X}=5)=\left(\begin{array}{c}7\\ 5\end{array}\right)\times (0.44{)}^5\times (0.66{)}^{7-5}\approx 0.10861$

$\mathrm{P}(\mathrm{X}=6)=\left(\begin{array}{c}7\\ 6\end{array}\right)\times (0.44{)}^5\times (0.66{)}^{7-6}\approx 0.0284$

$\mathrm{P}(\mathrm{X}=7)=\left(\begin{array}{c}7\\ 7\end{array}\right)\times (0.44{)}^7\times (0.66{)}^{7-7}\approx 0.00321$

$$\begin{gathered} P(x>4)=P(x=5)+P(x=6)+P(x=7) \\ =0.0186+0.0284+0.0032 \\ =0.1402 \\ =14.02\% \end{gathered}$$