Question

One card is drawn at random from a well-shuffled deck of 52 cards. In which of the following case is the events E and F independent?

E : ‘the card drawn is black’

F : ‘the card drawn is a king’

Answer 1

In a deck of 52 cards, 26 cards are black and 4 cards are kings.

∴ P(E) = P(the card drawn is black) = `26/52 = 1/2`

∴ P(F) = P(the card drawn is a king) = `4/52 = 1/13`

In the pack of 52 cards, 2 cards are black as well as kings.

∴ P (EF) = P(the card drawn is a black king) = `2/52 = 1/26`

⇒ P(E) × P(F) = P(EF)

⇒ `1/2 * 1/13 = 1/26`

Therefore, the given events E and F are independent.