Question

I WILL GIVE AN EXTRA 50 POINTS TO WHOEVER GETS THESE 2 QUESTIONS RIGHT

A card is drawn from a standard deck of cards. What is the probability
that a spade is drawn, then replaced, and a red card is drawn second?

A card is drawn from a standard deck of cards. What is the probability that a spade is drawn, NOT replaced, and another spade is drawn?

Answer 1

See below for answers and explanations

Explanation:

Problem 1:

A standard deck of cards contains 52 cards, consisting of 13 spades. If you select only one randomly, the probability of that occurring would be 13/52 or 1/4. Since there are only 26 red cards in a standard deck, then the probability of selecting a red card would be 26/52 or 1/2. Because the two events are independent of each other, their probabilities are multiplied. Therefore, the probability of selecting a spade, and then replacing it in hopes of drawing a red card is (1/2)(1/4) = 1/8.

Problem 2:

We are selecting a spade and then another spade while NOT replacing the first spade (remember that these events are independent of each other also). This means that the total card count will change by picking up the second card. Therefore, the probability of selecting a spade, followed by another spade, is (13/52)(12/51) = 156/2652 = 1/17.