Jeanne wants to start collecting coins and orders a coin collection starter kit. the kit comes with three coins chosen at random, each in a small envelope. each coin is either a nickel, a dime, or a quarter. use conditional probability to solve the following:

what is the probability that all three coins are quarters if the first two envelopes jeanne opens each contain a quarter?
what is the probability that all three coins are different if the first envelope jeanne opens contains a dime?

Conditional probability is a measure of the probability of an event given that another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B), or sometimes .

The conditional probability of event A happening, given that event B has happened, written as P(A|B) is given by


In the question, we were told that there are three randomly selected coins which can be a nickel, a dime or a quarter.

The probability of selecting one coin is

Part A:
To find the probability that all three coins are quarters if the first two envelopes Jeanne opens each contain a quarter, let the event that all three coins are quarters be A and the event that the first two envelopes Jeanne opens each contain a quarter be B.

P(A) means that the first envelope contains a quarter AND the second envelope contains a quarter AND the third envelope contains a quarter.

Thus

P(B) means that the first envelope contains a quarter AND the second envelope contains a quarter

Thus

Therefore,

Part B:
To find the probability that all three coins are different if the first envelope Jeanne opens contains a dime, let the event that all three coins are different be C and the event that the first envelope Jeanne opens contains a dime be D.





Therefore,