Question

A class has 8 GSIs. Each GSI tosses a coin 20 times and notes the number of heads. What is the probability that none of the GSIs gets exactly 10 heads?

Answer 1

Given that a class has 8 GSIs and that each GSI tosses a coin 20 times and notes the number of heads.

We need to find the probability that none of the GSIs gets exactly 10 heads.

Now probability of get a head in one toss of an unbiased coin p=1/5=0.5

Let,

X=Number of heads in 20 tosses of a coin

Binomial Distribution

A random variable X is said to have a binomial distribution if its PMF(Probability Mass Function) is given by,

where 0<p<1.

Notation: X~Binomial(n,p)

Coming back to our problem

Now the probability of getting exactly 10 heads in 20 tosses of a coin.

Hence the probability of getting exactly 10 heads in 20 tosses of a coin is 0.1762

Now we need to find the probability that none of the GSIs gets exactly 10 heads.

Probability that a GSI gets exactly 10 heads in 20 tosses of a coin p₁=0.1762

Let,

Y=Number of GSIs who get exactly 10 heads in 20 tosses of a coin out of the 8 GSIs

Now probability that none of the GSIs gets exactly 10 heads.

Hence the probability that none of the GSIs gets exactly 10 heads is 0.2121