If the probability is 0.65 that a marriage will end in divorce within 20 years, what is the probability that out of 7 couples just married in the next 20 years (A) None will be divorced?
(B) All will be divorced?
(C) Exactly 6 will be divorced?
(D) At least 6 will be divorced?

0.00064

0.049

0.185

0.234

Step-by-step explanation:

Using binomial distribution formula :

P(x = x) = nCx * p^x * (1 - p)^(n-x)

p = 0.65

1 - p = 1 - 0.65 = 0.35

n = 7

(A) None will be divorced?

P(x = 0) : 7C0 * 0.65^0 * 0.35^7

= 1 * 1 * 0.00064339296875

= 0.00064

(B) All will be divorced?

P(x = 7) : 7C7 * 0.65^7 * 0.35^0

1 * 0.04902227890625 * 1

= 0.049

(C) Exactly 6 will be divorced?

P(x = 6) : 7C6 * 0.65^6 * 0.35^1

7 * 0.075418890625 * 0.35

= 0.18477628203125

= 0.185

(D) At least 6 will be divorced?

P(x ≥ 6) = p(6) + p(7)

P(6) = 0.185

P(7) = 0.049

P(x ≥ 6) = 0.185 + 0.049 = 0.234