Question

a single card is drawn from a deck of 52 cards. find the probability that the card chosen is as follows.

the queen of spades or a black card.

Answer 1

Solution:

Given: A single card is drawn from a deck of 52 cards.

Find:

P( the queen of spades or a black card) =............?

Let A = Drawn card is  the queen of spades and B = Drawn card is  a black card

Thus we have to find:

P( A or B) = .............?

Using Addition rule of probability:

P( A or B) = P(A) + P(B) - P( A and B)

where

P(A) = P( Drawn card is  the queen of spades)

We have only one card out of 52 which is the queen of spades

thus

P(A) = 1/52

P(B) = Drawn card is  a black card

We have total 26 black cards

Thus

P(B) = 26/52

and

P( A and B) =P( Drawn card is  the queen of spades AND is  a black card )

Again there is only one card out of 52 which is the queen of spades and black card.

Thus

P(A and B) = 1/52

Thus

P( A or B) = P(A) + P(B) - P( A and B)

P( A or B) = 1/52 + 26/52 - 1/52

P( A or B) = 26/52

P( A or B) = 0.5

That is:

P( the queen of spades or a black card) = 0.5