For a group of 100 people, compute(a) the expected number of days of the year that are birthdays of exactly 3 people.(b) the expected number of distinct birthdays.

Step-by-step explanation:

Leaving leap years, a year contains 365 days.

For a group of 100 people, each person is independent of the other and probability of any day being his birthday has a chance of

a) Probability that  exactly 3 people have same birthday =

Each day is independent of the other

And hence no of days having exactly 3 persons birthday out of 100 persons is binomial with n = 365 and p =

Expected value of days = np =

b) Distinct birthdays is binomail with p =1/365 and n = 365

Hence

expected value = np =1

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have