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