Question
A card is drawn randomly from a deck of ordinary playing
cards. You win Rs.900 if the card is a spade or a king. What is the probability that you will win the game?Solution
Let S = the event that the card is a spade; and let A = the event that the card is a King. We know the following: There are 52 cards in the deck. There are 13 spades, so P(S) = 13/52. There are 4 King, so P(A) = 4/52. There is 1 King that is also a spade, so P(S ∩ A) = 1/52. Therefore, based on the rule of addition: P(S ∪ A) = P(S) + P(A) - P(S ∩ A) P(S ∪ A) = 13/52 + 4/52 - 1/52 = 16/52 = 4/13.
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