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Question
The king and queen of diamonds, queen and jack of hearts, jack and king of spades are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. Determine the probability that the card is a king of black card
Solution
King diamond + Queen diamonds = 1 + 1 = 2 ...(1)
Queen hearts + Jack of hearts = 1 + 1 = 2 ...(2)
Jack spade + King of spades = 1 + 1 = 2 ...(3)
Remaining number of cards = 52 – (6)
n(S) = 46
Let B be the event of getting a king of black card
n(B) = (2 – 1) ...[from (3) one black card is removed]
n(B) = 1
P(B) = `("n"("B"))/("n"("S")) = 1/46`
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