Alyssa is doing a card trick with one of her friends, Denise. She only uses 15 cards: 3 diamonds, 3 hearts, 4 spades, and 5 clubs. Denise draws one card, replaces it in the deck, and draws one card again.
What is the probability that she draws a heart both times?
How would you solve these particular problems???
since these events are independent of each other, you just multiply their probabilities.
Since there are 3 hearts out of 15 cards,
P(heart) = 3/15 = 1/5
P(heart,heart) = 1/5 * 1/5 = 1/25
1/25
To solve this problem, we need to understand the total number of possible outcomes and the favorable outcomes.
First, we need to determine the total number of possible outcomes. Alyssa has a deck of 15 cards, so there are 15 possible outcomes for the first draw.
Now, let's calculate the favorable outcomes. We know that Denise needs to draw a heart both times. There are 3 hearts in the deck, so for the first draw, there is a 3 out of 15 chance of drawing a heart.
After Denise replaces the card in the deck, there are still 15 cards, including 3 hearts. Therefore, for the second draw, there is also a 3 out of 15 chance of drawing a heart.
To find the probability of both events happening, we multiply the probabilities together. So the probability that Denise draws a heart both times is (3/15) * (3/15).
Solving this, (3/15) * (3/15) = 9/225 = 1/25.
Therefore, the probability that Denise draws a heart both times is 1/25, or approximately 0.04 or 4%.