A card is drawn at random from an ordinary deck of 52 playing cards. The probability that the card is a 10 or a spade is:

Concept:

• The probability of occurrence of an event A out a total possible outcomes N, is given by P(A) = \(\rm \dfrac{n(A)}{N}\), where n(A) is the number of ways in which event A can occur.
• For two events A and B we have P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Calculation:

Let's say that A is the event of drawing a 10 and B be the event of drawing a spade.

Probability of drawing a 10 = P(A) = \(\rm \dfrac{4}{52}\).

Probability of drawing a spade = P(B) = \(\rm \dfrac{13}{52}\).

Probability of drawing a 10 of spade = P(A ∩ B) = \(\rm \dfrac{1}{52}\).

∴ Probability of drawing a 10 or a spade = P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

= \(\rm \dfrac{4}{52}+\dfrac{13}{52}- \dfrac{1}{52}=\dfrac{16}{52}=\dfrac{4}{13}\).