Answer:0.182
Step-by-step explanation
Given
Probability that your detail match for any given topic is [tex]\frac{1}{50}[/tex]
There are n=10 topic
as no of topics are finite therefore we can use binomial distribution
Probability of success [tex]p=\frac{1}{50}=0.02[/tex]
Probability of failure [tex]q=1-p=\frac{49}{50}[/tex]
The formula For Probability Distribution for Binomial Distribution
[tex]P(X=r)=^nC_r(p)^r(q)^{n-r}[/tex]
Probability that at least one topic will be matched
[tex]P(X\geq 1)=1-P(X=0)[/tex]
[tex]P(X\geq 1)=1-^{10}C_{0}(0.02)^0(0.98)^{10}[/tex]
[tex]P(X\geq 1)=1-0.817=0.182[/tex]
