selected at random turns out to be good. Find the probability that a second item of the same lot will be defective if the first item is returned to the lot after it has been checked.

Bonnie and Connie are twins with identical purses. Bonnie needs 35 cents to pay for a parking meter. Suppose that Bonnie's purse has 5 quarters, 3 dimes, and 2 nickels while Connie's purse has 2 quarters, 5 dimes, and 3 nickels in it. Not being able to tell the difference between the purses, Connie picks one at random and grabs two coins from it. What is the probability that Bonnie picked her own purse given that she drew out enough change to pay for her parking meter? (Note: Bonnie needs to put in at least 35 cents to pay her parking meter.)

Suppose a jar contains 9 red marbles and 37 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.

Suppose 4 letters from a sign reading "Montreal" fell on the street. A mathematician find the 4 letters and randomly place them back on the sign (each of them on a spot where a letter fell off). What is the probability the sign reads "Montreal"?

Two cards are drawn from a standard deck without replacement. Find the probability that both cards are hearts.

If 14 people are randomly​ selected, find the probability that no 2 of them have the same birthday. Ignore leap years. The probability that 14 people have different birthdays is