CMIIh

2021-09-17

45% of the population has Type O blood. Find the probability that exactly 6 people in a group of 10 random people have Type O blood. Round your answer to six decimal places.

Ezra Herbert

Step 1
The binomial probability distribution is,
$P\left(X=x\right)=\left(beg\in \left\{array\right\}\left\{c\right\}n\mathrm{\setminus }xend\left\{array\right\}\right){\left(p\right)}^{x}{\left(1-p\right)}^{n-x}$
In the formula, n denotes the number of trails, p denotes probability of success, and x denotes the number of success.
The random variable X is defined as the number people have Type O blood which follows binomial distribution with sample size 10 and probability of success 0.45.
Step 2
The probability that exactly 6 people have Type O blood is,
$P\left(X=6\right)=\left(beg\in \left\{array\right\}\left\{c\right\}10\mathrm{\setminus }6end\left\{array\right\}\right){\left(0.45\right)}^{6}{\left(1-0.45\right)}^{10-6}$
$=210×0.0083037656×0.09150625$
$=0.159568$
Thus, the probability that exactly 6 people have Type O blood is 0.159568.

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