Question

If 500 people each select a number a random between 1 and 100, what is the probability
that 4 people select the number 25 ?

Answer 1

Answer on Question #38427 – Math – Other

The number 25 is selected from 1,2,...,100 with probability 0.01. Thus exact probability that 4 people select 25 is calculated using Binomial distribution with parameters $n=500$, $p=0.01$.

Let $\xi$ be a random variable that equals to number of people that selected 25. Then

$$\xi \sim B i (500, 0.01)$$ $$P(\xi = 4) = \binom{500}{4} 0.01^4 (1 - 0.01)^{500-4} = \binom{500}{4} 0.01^4 0.99^{496} = 0.175995$$