132k views
1 vote
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?

User Iamamac
by
8.9k points

1 Answer

3 votes

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).

User Sanjana
by
8.6k points