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Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.
- a)27/102
- b)29/102
- c)25/102
- d)23/102
Correct answer is option 'C'. Can you explain this answer?
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Two cards are drawn at random and without replacement from a pack of 5...
Required probability : P(BB) = P(B) X P(B/B) ……………{B means black card}
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Two cards are drawn at random and without replacement from a pack of 5...
To find the probability of drawing two black cards from a pack of 52 playing cards, we need to first determine the number of favorable outcomes and the total number of possible outcomes.
Number of Favorable Outcomes:
When we draw the first card, there are 26 black cards out of 52 in the deck. Therefore, the probability of drawing a black card on the first draw is 26/52.
After the first card is drawn, we have 51 cards remaining in the deck, with 25 black cards. So, the probability of drawing a black card on the second draw, without replacement, is 25/51.
To find the probability of both events occurring, we multiply the probabilities together:
P(Black card on first draw) × P(Black card on second draw) = (26/52) × (25/51)
Simplifying this expression:
(26/52) × (25/51) = (1/2) × (25/51) = 25/102
Therefore, the probability that both cards drawn are black is 25/102, which corresponds to option C.
Number of Favorable Outcomes:
When we draw the first card, there are 26 black cards out of 52 in the deck. Therefore, the probability of drawing a black card on the first draw is 26/52.
After the first card is drawn, we have 51 cards remaining in the deck, with 25 black cards. So, the probability of drawing a black card on the second draw, without replacement, is 25/51.
To find the probability of both events occurring, we multiply the probabilities together:
P(Black card on first draw) × P(Black card on second draw) = (26/52) × (25/51)
Simplifying this expression:
(26/52) × (25/51) = (1/2) × (25/51) = 25/102
Therefore, the probability that both cards drawn are black is 25/102, which corresponds to option C.
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Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.a)27/102b)29/102c)25/102d)23/102Correct answer is option 'C'. Can you explain this answer?
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