draws a card from a standard deck of 52 cards. She replaces the card and draws a second card. What is the probability that she draws a heart and then a spade?
well, each probability is 1/4, right?
To calculate the probability of drawing a heart and then a spade, we need to consider the number of favorable outcomes (the desired outcome) and the total number of possible outcomes.
There are 52 cards in a standard deck, and since she replaces the card after the first draw, the number of cards remains the same for the second draw.
First, let's calculate the probability of drawing a heart. In a standard deck, there are 13 hearts (one for each rank). So, the probability of drawing a heart on the first draw is 13/52, which simplifies to 1/4.
Next, let's calculate the probability of drawing a spade on the second draw. Similar to hearts, there are 13 spades in a standard deck. Therefore, the probability of drawing a spade (after replacing the card) is also 13/52, which simplifies to 1/4.
To find the probability of both events occurring (drawing a heart and then a spade), we multiply the probabilities together:
(1/4) * (1/4) = 1/16
Therefore, there is a 1/16 probability that she draws a heart and then a spade.