Question

A box contains one red, three blue, and two green marbles. Two marbles are selected at random in succession and without replacement. Let A={Both marbles selected are the same color.} Find P(A).

a) 1/14
b) 3/14
c) 4/14
d) 5/14

Answer 1

To find the probability of selecting two marbles of the same color, we divide the number of favorable outcomes by the total number of possible outcomes. The probability of event A is 1/14.

Step-by-step explanation:

To find the probability of event A, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes. In this case, the favorable outcomes are selecting two marbles of the same color. We can choose the two red marbles, two blue marbles, or two green marbles. This gives us a total of 3 favorable outcomes.

For the total number of possible outcomes, we need to consider that two marbles are selected without replacement. On the first draw, there are a total of 6 marbles in the box. After one marble is drawn, there are 5 remaining marbles. Therefore, the total number of possible outcomes is 6 * 5 = 30.

Finally, the probability of event A is given by P(A) = favorable outcomes / total outcomes = 3 / 30 = 1/10 = 1/14.