Question

7.20 Random Sampling with Coins Assume your class has 30 students and you want a random sample of 10 of them. A student suggests asking each student to flip a coin, and if the coin comes up heads, then he or she is in your sample. Explain why this is not a good method.

Answer 1

This a bad method because the probability that you will have a random sample of 10 students is = 30

What is Binomial Distribution?

The discrete probability distribution of the number of successes in a series of n separate experiments, each asking a yes-or-no question and each yielding a unique Boolean value: success or failure, is known as the binomial distribution with parameters n and p.

According to the given information:

P(X=10) = BINOM.DIST(10,30,0.5,FALSE)≈0.03

The likelihood that ten pupils will have heads after each toss has to be determined. Utilize the BINOM.DIST Excel formula. Four inputs are needed for the equation: the total number of successes, the total number of trials, the success probability, and either "true" for the total probability or "false" for the likelihood of an exact number of successes.

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

Substituting values,

P(X) = 30!/(10! * 20!) * (0.5)^10 * (0.5)^20

      = 0.03

This a bad method because the probability that you will have a random sample of 10 students is = 30

To know more about Binomial Distribution visit:

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