GATE CE 2015 Set 2 — Question 5
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Engineering Mathematics → Probability → Conditional Probability
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Question
Four cards are randomly selected from a pack of 52 cards. If the first two cards are kings, what is the probability that the third card is a king?
Correct answer
(B) 2/50
Solution
A standard deck contains 52 cards, including 4 kings.
Given that the first two cards drawn are kings, they are removed from the deck.
Remaining cards in the deck = .
Remaining kings in the deck = .
The probability that the third card selected is a king is the ratio of remaining kings to the total remaining cards:
.
Given that the first two cards drawn are kings, they are removed from the deck.
Remaining cards in the deck = .
Remaining kings in the deck = .
The probability that the third card selected is a king is the ratio of remaining kings to the total remaining cards:
.
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