Random Variable and Probability

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Asked: April 6, 20212021-04-06T08:59:06+00:00 2021-04-06T08:59:06+00:00In: High School/Senior Secondary School, Statistics and Probability

Random Variable and Probability

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Using the Discrete Probability Distribution, If five coins are tossed simultaneously, what is the probability of getting the five heads?

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acedstud · Answer 1 · 2021-04-06T20:21:23+00:00

The probability distribution of the number of outcomes from an event with only two possible outcomes is called a Binomial Probability Distribution.

The probability that a random variable $X$ which follows a binomial probability distribution is equal to the value $x$ is given by $P(X=x)=^nC_xp^x(1-p)^{n-x}$ , where $p$ is the probability of a favorable outcome (success) and $n$ is the total number of trials.

Here, $X$ is the random variable representing the number of heads that appears from the throw of the five coins and $p$ is the probability of getting a head in a single toss of a coin = 0.5.

Therefore, $P(X=5)=^5C_5(0.5)^5(1-0.5)^{5-5}=1\times0.03125\times1=0.03125$

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