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Question
Forty percent of business travellers carry a laptop. In a sample of 15 business travelers, what is the probability that 3 will have a laptop?
Solution
Given n = 5
p = `40/10 = 2/5`
q = 1 – p = `1 - 2/5 = (5-2)/5 = 3/5`
The binomial distribution P(X = x) = `15"c"_x (2/5)^x (3/5)^(15 - x)`
P(probability that 3 will have a laptop) = P(X = 3)
= `15"c"_3 (2/5)^3 (/5)^(15 - 3)`
= `(15 xx 14 xx 13)/(1 xx 2 xx 3) xx (2)^3/(5)^3 xx (3)^12/(5)^12`
= `455 xx (8 xx 5.311 xx 10^5)/(5)^15`
= `(3640 xx 5.311 xx 10^5)/(3.055 xx 10^10)`
= `(3640 xx 5.311)/(3.055 xx 10^5)`
= `19332.04/305500`
= 0.06328
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