# Ex 13.2, 15

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

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) = 152 Now, P(E) . P(F) = 14 × 113 = 152 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) = 252 = 126 Now, P(E) . P(F) = 12 × 113 = 126 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) = 452 = 113 Now, P(E) . P(F) = 1213 × 213 = 4169 Since P(E ∩ F) ≠ P(E) . P(F) Thus, E and F are not independent

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.