For a group of 50 people, assuming that each person is equally likely to have a birthday on each of 365 days in the year, compute
(a) The expected number of days of the year that are birthdays of exactly 3 people:

0.0177 days

Step-by-step explanation:

Solution:-

- The group has n = 50 people

- Each person is equally likely to have a birthday on each of 365 days in the year.

- The probability of success p = 1 / 365

- The probability of failure q = (1 - 1/365)

- We will denote random variable X as a given day has k number of birthdays.

- X follows binomial distribution:

                            X ~ Bi ( 50 , 1/365)

- The probability that there would be 3 birthdays on a day would be:

                           P ( X = 3 ) = 50C3 ( 1 / 365)^3 * ( 1 - 1/365)^47

                           P ( X = 3 ) = 0.00035

- The expected number of days for exactly three people to have same birth date:

                          E( X = 3 ) = P (X=3)*n = 0.00035*50 = 0.0177 days

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

the expression (1.26)2t reveals the approximate rate of increases in the number of plants semiannually.

hope this : )