Question

it has been estimated that 40% of marriages end in divorce. if you randomly select 9 recently married couples what is the probability that at least one of the marriages will end in divorce?
0.0101
0.9899
0.9744
0.1296

Explanation:

Step1: Find probability of no - divorce

The probability that a single marriage does not end in divorce is $1 - 0.4=0.6$. Since the couples are independent, the probability that none of the 9 marriages end in divorce is $(0.6)^{9}$.
$(0.6)^{9}=0.010077696$

Step2: Find probability of at least one divorce

The probability that at least one marriage ends in divorce is the complement of the event that none of the marriages end in divorce. Let $P(X\geq1)$ be the probability that at least one marriage ends in divorce. Then $P(X\geq1)=1 - P(X = 0)$.
$P(X\geq1)=1-(0.6)^{9}=1 - 0.010077696 = 0.989922304\approx0.9899$

Answer:

0.9899