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The probability of 2 seniors out of 20 serving in the military is ²⁰C₂(0.15)²(0.85)¹⁸.
What is a Binomial distribution?
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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