Sociologists say that 80% of married women claim that their husband\'s mother is
ID: 3056219 • Letter: S
Question
Sociologists say that 80% of married women claim that their husband's mother is the biggest bone of contention in their marriages sex and money are lower-rated areas of contention). Suppose that nine married women are having coffee together one morning. Find the following probabilities. (Round your answers to three decimal places.) (a) All of them dislike their mother-in-law. (b) None of them dislike their mother-in-law (c) At least seven of them dislike their mother-in-law d) No more than six of them dislike their mother-in-lawExplanation / Answer
Binomial Probability = nCx * (p)x * (q)n-x, where n = number of trials and x is the number of successes.
Here n = 9, p = 0.8 and q = 1 - p = 0.2
(a) P(x = 9) = 9C9 * (0.8)9 * (0.2)9-9 = 0.134
(b) P(x = 0) = 9C0 * (0.8)0 * (0.2)9-0 = 0.000 (It is actually 0.0000005)
(c) P( at least 7) = P(7) + P(8) + P(9) ...P(9) = 0.134 as found in (a)
P(7) = 9C7 * (0.8)7 * (0.2)9-7 = 0.302
P(8) = 9C8 * (0.8)8 * (0.2)9-8 = 0.302
Therefore P(7) + P(8) + P(9) = 0.302 + 0.302 + 0.134 = 0.738
(d) P(No more than 6) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1 - P(At least 7) = 1 - 0.738 = 0.262