A large bowl contains 1 million marbles Half of the marbles

A large bowl contains 1 million marbles. Half of the marbles have a plus (+) painted on them and the other half has a minus (?).

(a) If you randomly sample 10 marbles, one at a time with replacement from the bowl, what is the probability you will select 9 marbles with pluses and 1 with a minus?


(b) If you take 1000 random samples of 10 marbles, one at a time with replacement, how many of the samples would you expect to be all pluses?

Solution

Probability of plus is p = 1/2 = 0.5

q = 1-1/2 = 0.5

(a) If you randomly sample 10 marbles, one at a time with replacement from the bowl, what is the probability you will select 9 marbles with pluses and 1 with a minus?

From binom,inal distribution,

P(x=9) = 10C9 * 0.5^9 * 0.5^1 = 0.00976

(b) If you take 1000 random samples of 10 marbles, one at a time with replacement, how many of the samples would you expect to be all pluses?

5.98925781

So,

expected value is 5.98

All probabilities from

P(x=r) = nCr * p^r * q^(n-r)