Hiro has a stack of cards with one number from the set 1, 1, 2, 2, 3, 3, 3, 4 written on each card. what is the probability that he pulls out a 3 first and then pulls out a 2 without replacing them? 1/64 1/56 3/32 3/28

Total cards = 8

Probability of pulling number 3 card first = 3/8

Probability of pulling number 2 card second= 2/7

P(3, then 2) = (3/8)(2/7) = 3/28

3/28

 The correct option is (D)

Step-by-step explanation:  Given that Hiro has a stack of cards with one number from the set 1, 1, 2, 2, 3, 3, 3, 4 written on each card.

We are to find the probability that Hiro pulls out a 3 first and then pulls out a 2 without replacing them.

Let, 'S' be the sample space for the experiment.

Then, S = {1, 1, 2, 2, 3, 3, 3, 4}

⇒   n(S) = 8.

Let, 'E' and 'F' be the events of pulling a 3 and a 2 respectively.

Then, E = {3, 3, 3}  ⇒ n(E) = 3

and

F = {2, 2}  ⇒ n(F) = 2.

So, the probability that he pulls out a 3 is given by

and the probability that he pulls out a 2 without replacing the 3 is given by

Therefore, the probability that he pulls out a 3 first and then pulls out a 2 without replacing them is

Hence, the required probability is

Thus, (D) is the correct option.