Question

Three rotten apples are mixed with seven fresh apples. Find the probability distribution of the number of rotten apples, if three apples are drawn one by one with replacement. Find the mean of the number of rotten apples.

Answer 1

Given that rotten apples are 3 and fresh apples are 7.

Total apples = 10

Suppose X: no of rotten apples then X can take the values 0, 1, 2 and 3.

Now suppose E: getting a rotten apple

∴ P(E) = `3/10` and P(E') = `7/10`

Then P(X = 0) = P(E)P(E')P(E') = `343/1000`

P(X = 1) = 3P(E)P(E')P(E') = `441/1000`

P(X = 2) = 3P(E)P(E)P(E') = `189/1000`

P(X = 3) = P(E)P(E)P(E) = `27/1000`

Now, Mean = ΣXP(X)

= `0 xx 343/1000 + 1 xx 441/1000 + 2 xx 189/1000 + 3 xx 27/1000`

Mean = `900/1000`

= `9/10`