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Chapter 13 Class 12 Probability

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

Question 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^(π’βˆ’π’™) 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 (πŸ‘/πŸ’)^(πŸ“βˆ’π’™) (𝟏/πŸ’)^𝒙 P(all cards are spade) = 5𝐢5(1/4)^5 (3/4)^0 = (1/4)^5 =𝟏/πŸπŸŽπŸπŸ’ P(only three cards are spade) = 5𝐢3(1/4)^3 (3/4)^2 = 5!/(3! 2!) Γ— 9/1024 =πŸ’πŸ“/πŸ“πŸπŸ (iii) P(none of them are spade) = 5𝐢0(1/4)^0 (3/4)^5 = (3/4)^5 = πŸπŸ’πŸ‘/πŸπŸŽπŸπŸ’

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.