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Question

Two cards are drawn without replacement from a well shuffled pack. Find the probability that one of them is an ace of heart


A

125

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B

126

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C

152

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D

None of these

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Solution

The correct option is B

126


Find the required probability:

There are 52 cards in a pack of cards, but there is only 1 ace of hearts.

Let A be the event of getting an ace of hearts

pA=152

Let B be the event of not getting an ace of hearts

pB=5152

Two card are drawn. There are two ways of drawing the cards such that at least one of them is an ace of hearts

Case 1: Let C1 be the event where we draw the first card an ace of hearts and the second card as non ace of hearts

pC1=152×5151 [51 non ace of hearts remain in the remaining 51 cards]

pC1=152

Case 2: Let C2 be the event where we draw the first card as non ace of hearts and the second card as ace of hearts

pC2=5152×151 [1 ace of hearts remain in the remaining 51 cards]

pC2=152

Therefore, the total probability is pC1+pC2=152+152=126

So, the probability of getting an ace of hearts on drawing two cards from a full pack of cards is 126.

Hence, option (B) is the correct answer.


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