Question

sociologists say that 95%of married women claim that their husband's mother is the biggest bone of contention in their marriages. suppose that 12 married women are having coffee one morning. find the following probabilities.
All of them dislike their mother-in-law
none of them dislike their mother-in-law
at least 19 of them dislike their mother-in-law
no more than 9 of them dislike their mother-inlaw

Answer 1

Answer)

As there are fixed number of trials and probability of each and every trial is same and independent of each other

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 0.95

N = number of trials = 12

R = desired success

A)

All of them dislike their mother in law

P(12) = 12c12*(0.95^12)*(1-0.95)^12-12 = 0.54036008766

B)

P(0) = 12c12*(0.95^0)*(1-0.95)^12-0 = 0

C)

At least 9 = P(9) + P(10) + P(11) + P(12) = 0.99776359677

D)

P(no more than 9) = 1 - (p(10) + p(11) + p(12)) = 0.019568262