Question

Sociologists say that 85% 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 six married women are having coffee together one morning. Find the following probabilities. (Round your answers to three decimal places.) Find the probabilities for A-D

(a) All of them dislike their mother-in-law.

(b) None of them dislike their mother-in-law.


(c) At least four of them dislike their mother-in-law.


(d) No more than three of them dislike their mother-in-law

Answer 1

(A) 0.377,

(B) 0.000,

(C) 0.953,

(D) 0.047

Explanation:

We assume that having a bone of intention means not liking one's Mother-in-Law

(A) P(all six dislike their Mother-in-Law) = (85%)^6 = (.85)^6 = 0.377

(B) P(none of the six dislike their Mother-in-Law) =

(100% - 85%)^6 =

0.15^6 =

0.000

(C) P(at least 4 dislike their Mother-in-Law) =

P(exactly 4 dislike their Mother-in-Law) + P(exactly 5 dislike their Mother-in-Law) + P(exactly 6 dislike their Mother-in-Law) =

C(6,4) * (.85)^4 * (1-.85)^2 + C(6,5) * (.85)^5 * (.15)^1 + C(6,6) * (.85)^6 = (15) * (.85)^4 * (.15)^2 + (6) * (.85)^5 * .15 + (1) * (.85)^6 =

0.953

(D) P(no more than 3 dislike their Mother-in-Law) =

P(exactly 0 dislikes their Mother-in-Law) + P(exactly 1 dislikes her Mother) + P(exactly 2 dislike their Mother-in-Law) + P(exactly 3 dislike their Mother-in-Law) =

C(6,0) * (.85)^0 * (.15)^6 + C(6,1) * (.85)^1 * (.15)^5 + C(6,2) * (.85)^2 * (.15)^4 + C(6,3) * (.85)^3 * (.15)^3 =

(1)(1)(.15)^6 + (6)(.85)(.15)^5 + (15)(.85)^2 *(.15)^4 + (20)(.85)^3 * (.15)^3 =

0.047