What is the probability of first drawing a black card, then a three, and then a red card? Do not round your intermediate computations. Round your final answer to four decimal places.

Question

In a standard deck of 52, suppose a card is drawn at random from a standard deck. The card is then shuffled back into the deck. Then for a second time, a card is drawn at random from the deck. The card is then shuffled back into the deck. Finally, for a third time, a card is drawn at random from the deck.

Answer 1

So, 3 independent draws with replacement.

First draw is to get a club or a spade (p = 1/2)

Second draw is to get a three , any suit (p= 1/13)

Third draw is to get an heart or a diamond (p= 1/2)

Since order does matter and all three draws are independent we simply multiply and get 1/52