Question

A box contains 19 large marbles and 18 small marbles. Each marble is either green or white. 9 of the large marbles are green, and 8 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is small or green? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

It is given that a box contains 19 large marbles and 18 small marbles. Now, all the marbles are either green or white. It is given that 9 of the large marbles are green and 8 of the small marbles are white.

Thus, we can see that among 19 large marbles, 9 of them are green. Thus, the number of large marbles which are white are (19-9) = 10.

Thus, among the 19 large marbles, 9 of them are green and 10 are white.

Now, again, among the 18 small marbles, 8 of them are white. Thus, the number of small marbles which are green are (18-8) =10.

Thus, among the 18 small marbles, 8 of them are white and 10 are green.

Thus, probability of the marbles to be green marbles,

P(green) = 9/37 + 10/37 = 19/37

Probability of the marbles to be white marbles,

P(white) = 10/37 + 8/37 = 18/37

Now, the probability of marbles to be small and green,

P(small and green) = 10/37

We have, the probability of being small marbles,

P(small) = 18/37

We have to find the probability that if a marble is randomly selected from the box, it will be small or green.

Thus, P(small or green) = P(small) + P(green) - P(small and green) = 18/37 + 19/37 - 10/37 = (18+19-10)/37 = 27/37

=0.7297

Thus, the required probability is 0.7297.