This is a case of binomial distribution. The formula used in
calculations for binomial probability is:
P = nCr p^r
(1-p)^(n-r)
Where,
P = probability
nCr = combinations of
r from n possibilities
p = success rate = 40%
= 0.40
n = sample size = 10
<span>1st: Let us
calculate for nCr for r = 8 to 10. Formula is:</span>
nCr = n! / r! (n-r)!
10C8 = 10! / 8! 2! = 45
10C9 = 10! / 9! 1! = 10
10C10 = 10! / 10! 0! = 1
Calculating for probabilities when r = 8 to 10:
P (r=8) = 45 * 0.4^8 (0.6)^2 = 0.0106
P (r=9) = 10 * 0.4^9 (0.6)^1 = 0.0016
P (r=10) = 1 * 0.4^10 (0.6)^0 = 0.0001
Total probability that at least 8 were married = 0.0106 + 0.0016
+ 0.0001
Total probability
that at least 8 were married = 0.0123
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