Question

You have a bag with 6 marbles. One marble is white. You reach the bag 100 times. After taking out a marble, it is placed back in the bag. What is the probability of drawing a white marble at least once?

Answer 1

0.999999988

Explanation:

Given that you have a bag with 6 marbles. One marble is white. You reach the bag 100 times. After taking out a marble, it is placed back in the bag.

Because every time you replace the marble drawn, the probability for drawing a white marble in one draw is constant = p =5/6

No of trials n = 100

Here X no of times white marble is drawn is Binomial since there are two outcomes and also the probability is constant.

the probability of drawing a white marble at least once

=
`P(X\geq 1)\\=1-P(x=0)\\=1-((5)/(6) )^(100) \\=0.999999988`

Required probability is almost 1.