Statistics and Probability : Binomial Probability Distribution

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EyahTyro

Asked: April 12, 20212021-04-12T14:12:08+00:00 2021-04-12T14:12:08+00:00In: High School/Senior Secondary School, Statistics and Probability

Statistics and Probability : Binomial Probability Distribution

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A coin is a tossed 4 times. Find the probability that exactly 2 heads will appear.

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acedstud · Answer 1 · 2021-04-12T14:32:40+00:00

Let $X$ be a random variable representing the number of heads that appear in $n$ coin tosses, then the probability of success ( $p$ ) is $\dfrac{1}{2}=0.5$ .

The probability that a binomial distributed variable $X$ with the number of tries, $n$ , and the probability of success, $p$ is equal to a value $x$ is given by $P(X=x)=^nC_xp^x(1-p)^{n-x}$ .

Here, $n=4$ , so the probability that exactly two heads will appear ( $x=2$ ) is given by $P(X=2)=^4C_2(0.5)^2(1-0.5)^{4-2}=6\times0.25(0.5)^2=0.375$

Therefore, the probability that exactly two heads will appear is 0.375.

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