Question

A box contains 21 black, 15 red, and 4 purple marbles. Consider the two stage experiment of randomly selecting a marble from the box, not replacing it, then selecting a second marble. Determine the probabilities of the events below. ( A.) Selecting 2 black marbles (B.) Selecting 1 black then 1 purple marble (C.) Selecting 2 purple marbles

Answer 1

The probability of selecting 2 black marbles is 7/26. The probability of selecting 1 black then 1 purple marble is 7/130. The probability of selecting 2 purple marbles is 1/65.

Step-by-step explanation:

(A.) Selecting 2 black marbles:

The probability of selecting a black marble on the first draw is 21/40.

After not replacing the first marble, the probability of selecting a black marble on the second draw is 20/39.

Therefore, the probability of selecting 2 black marbles is (21/40) * (20/39) = 7/26.

(B.) Selecting 1 black then 1 purple marble:

The probability of selecting a black marble on the first draw is 21/40.

After not replacing the first marble, the probability of selecting a purple marble on the second draw is 4/39.

Therefore, the probability of selecting 1 black then 1 purple marble is (21/40) * (4/39) = 7/130.

(C.) Selecting 2 purple marbles:

The probability of selecting a purple marble on the first draw is 4/40.

After not replacing the first marble, the probability of selecting another purple marble on the second draw is 3/39.

Therefore, the probability of selecting 2 purple marbles is (4/40) * (3/39) = 1/65.