I need help answering the 4 questions below.

Question

Sociologists say that 90% 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 seven married women are having coffee together one morning. Find the following probabilities. (For each answer, enter a number. 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 five of them dislike their mother-in-law.

(d)

 No more than four of them dislike their mother-in-law.

Answer 1

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

P(a) = (90%) * (90%) * ... * (90%) [7 times, since there are 7 people]

= (90%)^7 = (90/100)^7 = (9/10)^7 = 9^7 / 10^7 = 9 * 81^3 / 10^7

= 4,782,969 / 10,000,000 = 0.478 [rounded to 3 decimal places]

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

P(b) = (100% - 90%) * ... * (100% - 90%) [7 times, since there are 7 people]

= (100% - 90%)^7 = (10%)^7 = (10/100)^7 = (1/10)^7 = 1^7 / 10^7

= 1 / 10,000,000 = 0.000 [rounded to 3 decimal places]

(c) At least five of them dislike their mother-in-law:

P(c) = (90%) * (90%) * ... * (90%) [5 times, since we want at least 5 people]

= (90%)^5 = (90/100)^5 = (9/10)^5 = 9^5 / 10^5 = 9 * 81^2 / 10^5

= 59,049 / 100,000 = 0.590 [rounded to 3 decimal places]

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

P(d) = 1 - P(c) [since we want at most 4 people aka less than 5 people]

= 1 - 59,049 / 100,000 = 100,000 / 100,000 - 59,049 / 100,000

= (100,000 - 59,049) / 100,000 = 40,951 / 100,000

= 0.410 [rounded to 3 decimal places]