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  1. Chapter 13 Class 12 Probability
  2. Serial order wise

Transcript

Ex 13.5, 4 Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that (i) all the five cards are spades? (ii) only 3 cards are spades? (iii) none is a spade?Let X : be the number of spade cards Drawing a card is a Bernoulli trial So, X has binomial distribution P(X = x) = nCx ๐’’^(๐’โˆ’๐’™) ๐’‘^๐’™ Here, n = number of cards drawn = 5 p = Probability of getting spade card = 13/52=1/4 q = 1 โ€“ p = 1 โ€“ 1/4=3/4 Hence, P(X = x) = 5Cx (๐Ÿ‘/๐Ÿ’)^(๐Ÿ“โˆ’๐’™) (๐Ÿ/๐Ÿ’)^๐’™ P(all cards are spade) = 5๐ถ5(1/4)^5 (3/4)^0 = (1/4)^5 =๐Ÿ/๐Ÿ๐ŸŽ๐Ÿ๐Ÿ’ P(only three cards are spade) = 5๐ถ3(1/4)^3 (3/4)^2 = 5!/(3! 2!) ร— 9/1024 =๐Ÿ’๐Ÿ“/๐Ÿ“๐Ÿ๐Ÿ (iii) P(none of them are spade) = 5๐ถ0(1/4)^0 (3/4)^5 = (3/4)^5 = ๐Ÿ๐Ÿ’๐Ÿ‘/๐Ÿ๐ŸŽ๐Ÿ๐Ÿ’

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.