There are 18 marbles in a bag, all of the same size. The marble; red, green and blue are in the ratio 2:3:4 respectively: if two marbles are selected at random one after the other and replaced, find the probability that all are blue

Answer 1

First, we need to find the probability of selecting a blue marble on the first draw.

The probability of selecting a blue marble on the first draw is the number of blue marbles divided by the total number of marbles.

There are 4 blue marbles out of 18 total marbles, so the probability of selecting a blue marble on the first draw is 4/18 = 2/9.

Since the marbles are replaced after each draw, the probability of selecting a blue marble on the second draw is also 2/9.

Therefore, the probability of selecting two blue marbles in a row is the product of the probabilities of selecting a blue marble on the first and second draw:

(2/9) * (2/9) = 4/81.

So, the probability that both selected marbles are blue is 4/81.