Michelle 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?
-First you must determine whether this is a permutation or combination problem.
*It is a permutation
-Next, use the formula permutation formula and plug in your variables.Solve.
*nPk= n!/(n-k)!
To find the probability that Michelle draws a Heart and then a Spade, we need to first determine the probability of drawing a Heart on the first card, and then the probability of drawing a Spade on the second card.
In a standard deck of 52 cards, there are 13 Hearts and 13 Spades. Since Michelle replaces the first card before drawing the second one, the probability of drawing a Heart on the first draw is:
P(Heart on first draw) = Number of Hearts / Total number of cards
= 13 / 52
= 1/4
After replacing the first card, there are still 52 cards in the deck, with 13 Spades. Therefore, the probability of drawing a Spade on the second card is:
P(Spade on second draw) = Number of Spades / Total number of cards
= 13 / 52
= 1/4
To find the probability of both events occurring, we multiply the probabilities together:
P(Heart and then Spade) = P(Heart on first draw) * P(Spade on second draw)
= (1/4) * (1/4)
= 1/16
Therefore, the probability that Michelle draws a Heart and then a Spade is 1/16.
The probability of a heart is 13/52 and for a spade = 13/52. The probability of both events occurring is found by multiplying the probabilities of the individual events.
13/52 * 13/52 = ?