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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’
Solution
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.
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