Question

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sara draws the 8 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 8.
$p(8 | 8\text{ of hearts}) = \square$
b. determine the probability that the second card is another heart.
$p(\text{heart}|8\text{ of hearts}) = \square$
c. determine the probability that the second card is a club.
$p(\text{club}|8\text{ of hearts}) = \square$
d. determine the probability that the second card is a 10.
$p(10 | 8\text{ of hearts}) = \square$

Explanation:

Step1: Calculate total remaining cards

After drawing the 8 of hearts, there are \(52 - 1=51\) cards left.

Step2: Calculate probability for part a

There are 3 remaining 8s (8 of spades, 8 of clubs, 8 of diamonds). So \(P(8|8\ of\ hearts)=\frac{3}{51}=\frac{1}{17}\).

Step3: Calculate probability for part b

There are \(13 - 1 = 12\) remaining hearts. So \(P(heart|8\ of\ hearts)=\frac{12}{51}=\frac{4}{17}\).

Step4: Calculate probability for part c

There are 13 clubs. So \(P(club|8\ of\ hearts)=\frac{13}{51}\).

Step5: Calculate probability for part d

There are 4 tens. So \(P(10|8\ of\ hearts)=\frac{4}{51}\).

Answer:

a. \(\frac{1}{17}\)
b. \(\frac{4}{17}\)
c. \(\frac{13}{51}\)
d. \(\frac{4}{51}\)