Ex 13.2, 15 (i) - Chapter 13 Class 12 Probability (Term 2)

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Ex 13.2, 15 One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent ? (i) E : ‘the card drawn is a spade’ F : ‘the card drawn is an ace’Two events A and B are independent if P(A ∩ B) = P(A) . P(B) One card is drawn at random from a well shuffled deck of 52 cards. E : the card drawn is a spade Number of spades = 13 Total number of cards = 52 P(E) = 13/52 = 1/4 F : the card drawn is an ace Number of ace = 4 Total number of cards = 52 P(F) = 4/52 = 1/13 E ∩ F = the card drawn is an ace of spades Number of ace of spades = 1 So, P(E ∩ F) = 1/52 Now, P(E) . P(F) = 1/4 × 1/13 = 1/52 Since, P(E ∩ F) = P(E) . P(F), Therefore, E and F are independent events