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 a king or queen’

F : ‘the card drawn is a queen or jack’

Answer 1

In a deck of 52 cards, 4 cards are kings, 4 cards are queens, and 4 cards are jacks.

∴ P(E) = P(the card drawn is a king or a queen) = `8/52 = 2/13`

∴ P(F) = P(the card drawn is a queen or a jack) = `8/52 = 2/13`

There are 4 cards which are king or queen and queen or jack.

∴ P(EF) = P(the card drawn is a king or a queen, or queen or a jack) = `4/52 = 1/13`

P(E) × P(F) = `2/13 * 2/13 = 4/169 ne 1/13`

⇒ P(E) · P(F) ≠ P(EF)

Therefore, the given events E and F are not independent.