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From an ordinary deck of cards, only 12 picture cards are retained. They are shuffled (mixed) and a man draws 2 cards at random. He then announce one of these cards is the King of Spades. What is the probability that he holds two Kings?
(A) 2/9
(B) 3/11
(C) 4/11
(D) 6/13
(E) 3/4
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
(A) 2/9
(B) 3/11
(C) 4/11
(D) 6/13
(E) 3/4
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
28 Jan 2021, 18:42
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12 picture cards has 4 Kings, 4 Queens and 4 Jacks in it.
If he is holding 1 king, the probability of getting the 1st King is 1.
We now have the remaining 11 cards in which there are 3 Kings.
Probability = Favorable Outcomes / Total Outcomes = \(\frac{3^C_1}{11^C_1} = \frac{3}{11}\)
If he is holding a spade, we are not sure if it is a king.
Probability = Favorable Outcomes / Total Outcomes = \(\frac{4^C_2}{12^C_2} = \frac{1}{11}\)
The required probability = 3/11 + 1/11 = 4/11
Option C
Arun Kumar
If he is holding 1 king, the probability of getting the 1st King is 1.
We now have the remaining 11 cards in which there are 3 Kings.
Probability = Favorable Outcomes / Total Outcomes = \(\frac{3^C_1}{11^C_1} = \frac{3}{11}\)
If he is holding a spade, we are not sure if it is a king.
Probability = Favorable Outcomes / Total Outcomes = \(\frac{4^C_2}{12^C_2} = \frac{1}{11}\)
The required probability = 3/11 + 1/11 = 4/11
Option C
Arun Kumar
16 Dec 2021, 22:56
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Bunuel
Kindly share the solution.
