5. It is known that 15% of the seniors in a large high school enter military
service upon graduation. If a group of 20 seniors are randomly selected,
what is the probability of observing two who will be entering military
service? *

Answer:

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The probability of 2 seniors out of 20 serving in the military is ²⁰C₂(0.15)²(0.85)¹⁸.

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

As it is given that 15% of the seniors in a large high school enter military

service upon graduation. Therefore, the probability of a large high school entering the military services will be 0.15. Similarly, the probability of a senior from a large high school not joining entering the military can be written as,

[tex]q = (1-p)\\\\q = 1-0.15\\\\q=0.85[/tex]

Now, the probability of 2 seniors out of 20 serving in the military will be,

[tex]P(x) = ^nC_x p^xq^{(n-x)}\\\\P(x=2) = ^{20}C_2 \times (0.15)^2 \times (0.85)^{(20-2)}\\\\P(x=2) = ^{20}C_2 \times (0.15)^2 \times (0.85)^{(18)}[/tex]

Hence, the probability of 2 seniors out of 20 serving in the military is ²⁰C₂(0.15)²(0.85)¹⁸.

Learn more about Binomial Distribution:

https://brainly.com/question/14565246

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