FOUR DECIMAL ANSWERS 3 You are charged with the responsibili

FOUR DECIMAL ANSWERS

3. You are charged with the responsibility to determine the probability of coincidental birthdays. Initially the following two birthday questions were assigned to you.

a. Ignoring leap years, find the probability that two randomly chosen people were born on January 1.

b. Ignoring leap years, find the probability that two randomly selected people have the same birthday.

c. You have a bag containing 1 red ball, 2 blue balls, 3 yellow balls, 4 black balls and 5 white balls. What is the probability of drawing without replacement a red ball, then a blue ball and lastly a yellow ball in the first three draws?

d. For problem 3c how many different combinations are possible for the draw?

e. For problem 3c how many different permutations are possible for the draw?

Solution

A.) 0.0007506098% or 1/(365^2)

365 days in a year, so the chance of 2 people born on Jan 1st is (1/365) * (1/365) = 1 / (365^2)

B.) 0.274% or 1 in 365

Since the date doesn\'t matter, the chance that the birthdates match is simply 1/365. (The answer to Part A times 365 possible matching dates.)

C.) 0.2198% or 6/2730

1red ball *2 blue balls * 3 yellow balls divided by:

15 balls remaing, 14 balls remaining, 13 balls remaining

(1 * 2 * 3) / (15 * 14 * 13) = 6 / 2730

D.) 455

nCr = n! / (n-r)! * r!

15C3 = 15! / (12! * 3!) = (15 * 14 * 13) / (3 * 2) = 2730 / 6 = 455

E.) 2730

nPr = n! / (n-r)!

15P3 = 15! / (15-3)! = 15! / 12! = 15 * 14 * 13 = 2730