Check sibling questions

Ex 13.5, 4 - Five cards are drawn successively from pack

Ex 13.5, 4 - Chapter 13 Class 12 Probability - Part 2
Ex 13.5, 4 - Chapter 13 Class 12 Probability - Part 3
Ex 13.5, 4 - Chapter 13 Class 12 Probability - Part 4

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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 𝒒^(𝒏−𝒙) 𝒑^𝒙 Here, n = number of cards drawn = 5 p = Probability of getting spade card = 13/52=1/4 q = 1 – p = 1 – 1/4=3/4 Hence, P(X = x) = 5Cx (𝟑/𝟒)^(𝟓−𝒙) (𝟏/𝟒)^𝒙 P(all cards are spade) = 5𝐶5(1/4)^5 (3/4)^0 = (1/4)^5 =𝟏/𝟏𝟎𝟐𝟒 P(only three cards are spade) = 5𝐶3(1/4)^3 (3/4)^2 = 5!/(3! 2!) × 9/1024 =𝟒𝟓/𝟓𝟏𝟐 (iii) P(none of them are spade) = 5𝐶0(1/4)^0 (3/4)^5 = (3/4)^5 = 𝟐𝟒𝟑/𝟏𝟎𝟐𝟒

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.