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From a pack of 52 cards, 2 cards are drawn at random. What is the probability that both cards are black card or heart card?
- a)31/102
- b)21/73
- c)1/5
- d)17/100
- e)3/10
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
From a pack of 52 cards, 2 cards are drawn at random. What is the prob...
Prob. of black card:
26C2 / 52C2 = 25/102
Prob. of heart card:
13C2 / 52C2 = 3/51
Add both cases.
26C2 / 52C2 = 25/102
Prob. of heart card:
13C2 / 52C2 = 3/51
Add both cases.
Most Upvoted Answer
From a pack of 52 cards, 2 cards are drawn at random. What is the prob...
Answer is 1/26 because in Dec of 52 card their are 26 black cards and 26 blue
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From a pack of 52 cards, 2 cards are drawn at random. What is the prob...
Solution:
To find the probability that both cards are either black or heart, we need to find the number of favorable outcomes and the total number of possible outcomes.
Favorable Outcomes:
There are 26 black cards in a deck of 52 cards (clubs and spades) and 13 heart cards. However, we need to subtract the 2 black heart cards (the Ace of Hearts and the King of Hearts) as they are counted in both categories.
Therefore, the number of favorable outcomes = 26 (black cards) + 13 (heart cards) - 2 (black heart cards) = 37.
Total Outcomes:
When we draw 2 cards from a deck of 52 cards, the total number of possible outcomes can be calculated using the combination formula:
Total number of outcomes = C(52, 2) = (52!)/(2!(52-2)!) = (52!)/(2!50!) = (52*51)/(2*1) = 1326.
Probability:
The probability of an event is defined as the favorable outcomes divided by the total outcomes.
Therefore, the probability that both cards drawn are either black or heart = Favorable outcomes / Total outcomes = 37 / 1326 = 31/102.
Hence, the correct answer is option A) 31/102.
To find the probability that both cards are either black or heart, we need to find the number of favorable outcomes and the total number of possible outcomes.
Favorable Outcomes:
There are 26 black cards in a deck of 52 cards (clubs and spades) and 13 heart cards. However, we need to subtract the 2 black heart cards (the Ace of Hearts and the King of Hearts) as they are counted in both categories.
Therefore, the number of favorable outcomes = 26 (black cards) + 13 (heart cards) - 2 (black heart cards) = 37.
Total Outcomes:
When we draw 2 cards from a deck of 52 cards, the total number of possible outcomes can be calculated using the combination formula:
Total number of outcomes = C(52, 2) = (52!)/(2!(52-2)!) = (52!)/(2!50!) = (52*51)/(2*1) = 1326.
Probability:
The probability of an event is defined as the favorable outcomes divided by the total outcomes.
Therefore, the probability that both cards drawn are either black or heart = Favorable outcomes / Total outcomes = 37 / 1326 = 31/102.
Hence, the correct answer is option A) 31/102.
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