In bowling you have two chances to knock down all the pins I

In bowling you have two chances to knock down all the pins. I am a terrible bowler. At my best, I can roll two strikes (knock down all the pins on the first roll) out of ten frames. On my second roll I can finish off the pins at a slightly better rate, knocking down the remaining pins in four out of ten tries. What is the probability that I will knock down all the pins on any particular frame (out of two rolls)?

Solution

P(knocking remaining pins is second roll) = 4/10 = 0.4

Number of frames where he rools second time = 10-2 =8

P( that he will knock down all the pins on any particular frame) = 8/10 * 0.4 = 0.32 Answer