Suppose that each time John throws a basketball he has a 25% probability of making the shot, independent of all other attempts. If John shoots the ball 7 times, what is the probability he will succeed exactly 4 times? Please begin by defining a probability space.

Solution Each outcome can be represented by a sequence of 7 letters: S(score) or M(miss). For example one possible outcome is: Sample space S =SMSMMSS Pr(score in any single attemt)= 0.25 Pr(miss) =1 0.25 = 0.75 Since each attempt is independent, we can use the binomial distribution to calculate the prob- ability of succeeding exactly 4 times out of 7 attempts: Pr(Scoring exactly 4 times in 7 attempts) = (7 choose 4) (0.25)4 (0.75)3 = 35 0.00390625 0.421875 =0.369140626 Therefore, the probability of John succeeding exactly 4 times out of 7 attempts is approximately 0.369 or 36.9%

Is it the right way to solve this?