Question

Suppose that you are seated next to a stranger on an airplane and you start discussing various topics such as where you were born (what state or country), what your favorite movie of all time is, your spouse's occupation, and so on. For simplicity, assume that the probability that your details match for any given topic is 1/50 and is independent from one topic to the next. If you discuss 10 topics, how surprising would it be to find that you match on at least one of them?

Answer 1

Answer:0.182

Explanation

Given

Probability that your detail match for any given topic is
`(1)/(50)`

There are n=10 topic

as no of topics are finite therefore we can use binomial distribution

Probability of success
`p=(1)/(50)=0.02`

Probability of failure
`q=1-p=(49)/(50)`

The formula For Probability Distribution for Binomial Distribution

`P(X=r)=^nC_r(p)^r(q)^(n-r)`

Probability that at least one topic will be matched

`P(X\geq 1)=1-P(X=0)`

`P(X\geq 1)=1-^(10)C_(0)(0.02)^0(0.98)^(10)`

`P(X\geq 1)=1-0.817=0.182`