Question 765442: A card is drawn from a well-shuffed deck of 52 cards. Find the probability that the card is a black card or a five.
Answer by ramkikk66(644)   (Show Source):
You can put this solution on YOUR website! A card is drawn from a well-shuffed deck of 52 cards. Find the probability that the card is a black card or a five.
No. of cards in deck = 52
No. of black cards = 26 (Two suits of spades, clubs)
So, Probability of drawing a black card = 26/52 = 1/2
No. of 5's = 4 (one 5 in each suit)
So, Probability of drawing a 5 = 4/52 = 1/13
But here's the catch - there are 2 cards which are both black and 5 (5 of
spades, and 5 of clubs). These 2 would get counted twice in both the above sets. We need to subtract that.
No. of cards which are both black and 5 = 2 (5 of spades, 5 of clubs)
Probability of drawing a black 5 = 2/52 = 1/26
Hence, no of possibilities of getting a black OR 5 =
Probability of drawing a black +
probability of drawing a five -
probability of drawing a black 5
= 1/2 + 1/13 - 1/26 = (13 + 2 - 1)/26 = 14/26 = 7/13
Hope you got it :)
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