Mathematics: It is estimated that one third of the general population has blood type a a sample of six people is selected at random. what is the probability that exactly three of them have blood type a?

It is estimated that one third of the general population

Ответ:

chriscook4471

12.03.2022

Mathematics

0.2195

Step-by-step explanation:

Binomial distribution formula :-

$P(x)=^nC_xp^x(1-p)^{n-x}$ , where P(x) is the probability of x successes in the n independent trials of the experiment and p is the probability of success.

Given : The probability of that the general population has blood type A = $\dfrac{1}{3}$

Sample size : n=6

Now, the probability that exactly three of them have blood type A is given by :-

$P(3)=^6C_3(\dfrac{1}{3})^3(1-\dfrac{1}{3})^{6-3}\\\\=\dfrac{6!}{3!3!}(\dfrac{1}{3})^3(\dfrac{2}{3})^{3}\\\\=0.219478737997\approx0.2195$

Therefore, the probability that exactly three of them have blood type A = 0.2195

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It is estimated that one third of the general population has blood type a a sample of six people is selected at random. what is the probability that exactly three of them have blood type a?

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