Question

There are 52 white keys and 36 black keys on a standard piano. What is the probability that if a person did not look and hit the keyboard twice that he or she would first hit a white key and then hit a black key?

Answer 1

Answer: The required probability is
`(117)/(484).`

Step-by-step explanation: Given that there are 52 white keys and 36 black keys on a standard piano. A person did not look and hit the keyboard twice.

We are find the probability that the person first hit a white key and hit a black key.

Let A and B represents the events that the person hit a white key and a black key respectively.

Then, the probabilities of events A and B are given by

`P(A)=(52)/(52+36)=(52)/(88),\\\\\\P(B)=(36)/(52+36)=(36)/(88).`

Since the events A and B are independent of each other, so the probability that the person first hit a white key and hit a black key is given by

`P(A\cap B)=P(A)* P(B)=(52)/(88)*(36)/(88)=(13)/(22)*(9)/(22)=(117)/(484).`

Thus, the required probability is
`(117)/(484).`