Question 16

What is the probability of drawing a king or a heart from a deck of cards ?

Solution

Probability of A or B = Probability of A + Probability of B - Probability of A and B.

$$\Rightarrow$$ Probability of drawing king or heart = Probability of drawing king + Probability of drawing heart - Probability of drawing kings which are hearts from the deck of cards.

A deck of cards contain 52 cards, of which there are 4 kings and 13 hearts and 1 king which is heart also. 

Probability of drawing a king = $$\frac{4}{52}$$

Probability of drawing a heart = $$\frac{13}{52}$$

Probability of drawing a king which are heart also = $$\frac{1}{52}$$

$$\Rightarrow$$ Probability of drawing king or heart = $$\frac{4}{52} + \frac{13}{52} - \frac{1}{52}$$

= $$\frac{16}{52}$$

= $$\frac{4}{13}$$

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