Ben has a batting average of 0333 so at bat the probability

Ben has a batting average of 0.333, so at bat the probability of him getting a hit is p = 1/3 and all at bats are independent of one another. If Ben gets to the plate four times, what is the probability that he gets at least one hit in a given game? What is the probability that he gets at least one hit in each of 66 consecutive games?

Solution

a) probability of hitting atleast once = 1 - probably of hitting 0 time

= 1 - 2/3*2/3*2/3*2/3

= 1 - 16/81

= 65/81 = 0.80247

b) the probability that he gets at least one hit in each of 66 consecutive games = (0.80247)⁶⁶ = 4.92346 x 10^-7