Question 1210425: Sara draws the 3 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 3.
P(3 3 of hearts) =
b. Determine the probability that the second card is another heart.
P (heart 3 of hearts) =
c. Determine the probability that the second card is a club.
P (club 3 of hearts) =
d. Determine the probability that the second card is a 7.
P(7 / 3 of hearts) =
Write your answers as reduced fractions.
Answer by math_tutor2020(3822)   (Show Source):
You can put this solution on YOUR website!
Answers:
(a) 1/17
(b) 4/17
(c) 13/51
(d) 4/51
Explanations
Part (a)
There are 4 copies of cards with the label "3" (one for each suit).
Since Sara is not replacing the 3 of hearts she selects, there are 4-1 = 3 copies remaining. This is out of 52-1 = 51 cards.
3/51 = (1*3)/(17*3) = 1/17 is the probability of another 3 being selected if the first card is not replaced.
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Part (b)
There are 52 cards in a deck.
52/4 = 13 of which are hearts
(ace, 2 through 10, jack, queen, king)
This excludes jokers.
If 3 of hearts is the first card, and not put back or replaced, then there would be 13-1 = 12 hearts remaining out of 52-1 = 51 cards
12/51 = (4*3)/(17*3) = 4/17 is the answer to part (b)
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Part (c)
There are 13 clubs out of 52-1 = 51 cards remaining.
This leads directly to 13/51 which cannot be reduced further.
Note I did not subtract 1 from the clubs since the sets "hearts" and "clubs" are mutually exclusive. There's no overlap.
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Part (d)
There are 4 copies of 7 out of 52-1 = 51 cards remaining.
Therefore the answer is 4/51
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