Ex 13.2, 15 - Chapter 13 Class 12 Probability

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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 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