Ex 13.2, 15

Transcript

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 ∩ 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 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 ? (ii) E : ‘the card drawn is black’ F : ‘the card drawn is a king’ 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 ∩ F = the card drawn is a black king Number of black king = 2 So, P(E ∩ F) = 2﷮52﷯ = 1﷮26﷯ Now, P(E) . P(F) = 1﷮2﷯ × 1﷮13﷯ = 1﷮26﷯ Since, P(E ∩ F) = P(E) . P(F), Therefore, E and F are independent events 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 ? (iii) E : ‘the card drawn is a king or queen’ F : ‘the card drawn is a queen or jack’. 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 ∩ F = the card drawn is a king or queen & queen or jack E ∩ F = the card drawn is a queen So, P(E ∩ F) = 4﷮52﷯ = 1﷮13﷯ Now, P(E) . P(F) = 12﷮13﷯ × 2﷮13﷯ = 4﷮169﷯ Since P(E ∩ F) ≠ P(E) . P(F) Thus, E and F are not independent