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 $\dfrac{117}{484}.$

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

$P(A)=\dfrac{52}{52+36}=\dfrac{52}{88},\\\\\\P(B)=\dfrac{36}{52+36}=\dfrac{36}{88}.$

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

$P(A\cap B)=P(A)\times P(B)=\dfrac{52}{88}\times\dfrac{36}{88}=\dfrac{13}{22}\times\dfrac{9}{22}=\dfrac{117}{484}.$

Thus, the required probability is $\dfrac{117}{484}.$