# Ex 13.2, 15 - Chapter 13 Class 12 Probability

Last updated at Dec. 8, 2020 by Teachoo

Last updated at Dec. 8, 2020 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 : 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 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 : ‘thea 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 : the card drawn is a black Number of black cards = 26 Total number of cards = 52 P(E) = 26/52 = 1/2 F : the card drawn is an king Number of king cards = 4 Total number of cards = 52 P(F) = 4/52 = 1/13 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’.E : the card drawn is king or queen Number of kings or queen = 4 + 4 = 8 Total number of cards = 52 P(E) = 8/52 = 2/13 F : the card drawn is queen or jack Number of queen or jack = 4 + 4 = 8 Total number of cards = 52 P(F) = 8/52 = 2/13 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

Ex 13.2

Ex 13.2, 1

Ex 13.2, 2

Ex 13.2, 3 Important

Ex 13.2, 4

Ex 13.2, 5

Ex 13.2, 6

Ex 13.2, 7 Important

Ex 13.2, 8 Important

Ex 13.2, 9 Important

Ex 13.2, 10 Important

Ex 13.2, 11 Important

Ex 13.2, 12

Ex 13.2, 13 Important

Ex 13.2, 14 Important

Ex 13.2, 15 Important You are here

Ex 13.2, 16 Important

Ex 13.2, 17

Ex 13.2, 18 Important

Chapter 13 Class 12 Probability

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.