


Binomial Distribution
Ex 13.5, 12 Deleted for CBSE Board 2022 Exams
Ex 13.5, 2 Deleted for CBSE Board 2022 Exams
Ex 13.5, 4 Important Deleted for CBSE Board 2022 Exams You are here
Ex 13.5, 9 Deleted for CBSE Board 2022 Exams
Ex 13.5, 6 Important Deleted for CBSE Board 2022 Exams
Ex 13.5, 11 Deleted for CBSE Board 2022 Exams
Ex 13.5, 14 (MCQ) Important Deleted for CBSE Board 2022 Exams
Ex 13.5, 15 (MCQ) Important Deleted for CBSE Board 2022 Exams
Example 32 Important Deleted for CBSE Board 2022 Exams
Ex 13.5, 13 Important Deleted for CBSE Board 2022 Exams
Ex 13.5, 3 Important Deleted for CBSE Board 2022 Exams
Misc 6 Important Deleted for CBSE Board 2022 Exams
Misc 7 Important
Ex 13.5, 7 Important Deleted for CBSE Board 2022 Exams
Example 31 Important Deleted for CBSE Board 2022 Exams
Ex 13.5, 5 Deleted for CBSE Board 2022 Exams
Ex 13.5, 10 Important Deleted for CBSE Board 2022 Exams
Misc 5 Important Deleted for CBSE Board 2022 Exams
Misc 9 Deleted for CBSE Board 2022 Exams
Misc 4 Deleted for CBSE Board 2022 Exams
Misc 10 Important
Example 35 Deleted for CBSE Board 2022 Exams
Ex 13.5, 8 Deleted for CBSE Board 2022 Exams
Example 34 Deleted for CBSE Board 2022 Exams
Binomial Distribution
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