Question

A card is selected from a shuffled deck. What is the probability that it is either a king or a club? That it is both a king and a club?

Short answer

The probability that the card is either a king and a club is 1/52 and the probability that the number is either a king and a club or both is 4/13.

Step-by-step solution

Expression for the probability that either one of the events will occur

The expression for the probability that either one of the events will occur is as follows,

P(A + B) = P(A) + P(B) -P(AB)

Here, P(A) is one event, and P(B) is another event.

Determination of the probability that the card is either a king and a club

In a deck of card, there are 52 cards of 4 suits namely spade, club, diamond and heart, out of which spade and club are black and diamond and heart are red.

There are 13 cards of each suit and 26 cards of each color.

Let A represents the event that card is king and B represents the event that card is club.

In a deck, there are 13 club cards, out of which only one is king, So, the probability is as follows,

P(AB) = 1/52

Thus, the probability that the number is either a king and a club or both is 1/52.

Determination of the probability that the card is either a king and a club or both

Write the probability that there are 4 king cards.

P(A) = 4/52

Write the probability that there are 13 club cards.

P(B) = 13/52

Write the expression for the probability that the card is either a king and a club or both.

P(A + B) = P(A) + P(B) -P(AB)

Substitute all the values in the above expression.

P (A + B) = (4/52) + (13/52) - (1/52)

= 16/52

= 4/13

Thus, the probability that the card is either a king and a club or both is 4/13.