Question

Sara draws the 2 of hearts from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card.

a. Determine the probability that the second card is another
2. P(2 | 2 of hearts) =

b. Determine the probability that the second card is another heart.
P(heart 2 of hearts) =

C. Determine the probability that the second card is a club.
P(club 2 of hearts) =

d. Determine the probability that the second card is a 9.
P(9 | 2 of hearts) =
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Answer 1

The probabilities after drawing a 2 of hearts without replacement from a deck of 52 cards are 1/17 for another 2, 12/51 for another heart, 13/51 for a club, and 4/51 for a 9.

Step-by-step explanation:

The question involves calculating the probability of drawing a specific card from a standard deck of 52 cards after having already drawn 2 hearts, without replacing the first card. The computations use the fundamental rules of probability, accounting for the changed deck size after the first draw.

Answers:

Probability of drawing another 2 (P(2 | 2 of hearts)): Since the 2 of hearts have already been drawn, there are only three 2s left in a deck now containing 51 cards. Thus, the probability is 3/51 or 1/17.

Probability of drawing another heart (P(heart | 2 of hearts)): With the 2 of hearts gone, there are 12 hearts left in the deck. Therefore, the probability is 12/51.

Probability of drawing a club (P(club | 2 of hearts)): All 13 clubs are still in the deck, so the probability is 13/51.

Probability of drawing a 9 (P(9 | 2 of hearts)): There are four 9s in a full deck, but since one card is missing, the probability is 4/51.

Answer 2

To determine the probability of drawing a specific card as the second card without replacement, we need to consider the number of cards left in the deck and the number of favorable outcomes for each event.

Step-by-step explanation:

To determine the probability of drawing a specific card as the second card, we need to consider the number of cards left in the deck and the number of favorable outcomes for each event.

a. P(2 | 2 of hearts): There are 51 cards left in the deck after drawing the 2 of hearts. Since there is only one 2 left in the deck, the probability of drawing another 2 is 1/51.

b. P(heart | 2 of hearts): There are 51 cards left in the deck after drawing the 2 of hearts. There are 12 remaining hearts in the deck, so the probability of drawing another heart is 12/51.

c. P(club | 2 of hearts): Since the 2 of hearts is not a club, there are still 13 clubs left in the deck. So, the probability of drawing a club as the second card is 13/51.

d. P(9 | 2 of hearts): There are 51 cards left in the deck after drawing the 2 of hearts. There are four 9s remaining, so the probability of drawing a 9 is 4/51.