Question

he probability that an individual has​ 20-20 vision is 0.13. In a class of 24 ​students, what is the probability of finding five people with​ 20-20 vision

Answer 1

Answer: 0.111947

Step-by-step explanation:

Let x be a binomial variable that represents the number of people with​ 20-20 vision.

Given: The probability that an individual has​ 20-20 vision: p= 0.13

Sample size : n= 24

Binomial probability distribution formula:

$P(X=x)=^nC_xp^x(1-p)^{n-x}$

The probability of finding five people with​ 20-20 vision :

$P(X=5)=\ ^{24}C_5(0.13)^5(1-0.13)^{24-5}\\\\=\dfrac{24!}{5!19!}(0.13)^5(0.87)^{19}\\\\=0.111946975387\approx0.111947$

Hence, the required probability = 0.111947

Answer 2

The probability of finding five people with 20-20 vision is 0.0461.

Binomial Probability:

The formula for the Binomial Probability is,

$P(X = x) =(\frac{n!}{x!(n-x)!} )\times p^x \times (1-p)^{n-x}$

Given that,

$p = 0.13\\1 - p = 0.87\\n = 72\\x = 5$

Substituting the given values into the above formula we get,

$P(X = x) =(\frac{n!}{x!(n-x)!} )\times p^x \times (1-p)^{n-x}\\P(X=5)=(\frac{72!}{5!(72-5)!} ) (0.13)^5(0.87)^{72-5}\\P(X=5)=0.0461$

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