In a situation where there are 25 students in a class (studentsare numbered from 1...

In a situation where there are 25 students in a class (students are numbered from 1 to 25) and they each have random birthdays so every birthday has a probability of 1/365, there is an event E[a, b] where a and b is each pair of students.

1. How many possible events are there and what is the probability of each one?

2. What is the expected number of pairs of students who would share a birthday (using linearity of expectation)?

3. Would the number of pairs who share a birthday be a binomial random variable?

Solutions

Expert Solution

no. of events = no. of pairs

= no. of ways to select 2 students out of 25

= 25C2

= 300

P(pair has same birthday) = P(2 nd student has same birthday as 1st)

= 1/365

Expected no/ of pairs with same birthday = no. of pairs * P(pair has same birthday)

= 300 * (1/365)

= 0.8219

YES,

the number of pairs who share a birthday be a binomial random variable

because each pairs probability of having same birthday is independent of each other and there only two outcomes : success(same birthday) , fail(different birthdays)

orchestra answered 2 years ago

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