Answer: The required probability is [tex]\dfrac{117}{484}.[/tex]
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
[tex]P(A)=\dfrac{52}{52+36}=\dfrac{52}{88},\\\\\\P(B)=\dfrac{36}{52+36}=\dfrac{36}{88}.[/tex]
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
[tex]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}.[/tex]
Thus, the required probability is [tex]\dfrac{117}{484}.[/tex]
