Find the probability

Question

At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 29 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon.

Find the probability that fifteen do not use the foil as their main weapon. (Round your answer to four decimal places.)

Answer 1

P(X=r) = C(n,r)·p^rq^n-r where q=1-p=1-0.60=0.40

If we are to find the probability that 15 do not use the foil as their main weapon, then this is the same as the probability of 14 that do use the foil as their main weapon:

P(X=14) = C(29,14)·(0.60)¹⁴(0.40)^29-14 ≈ 0.0653

Therefore, the probability that fifteen do not use the foil as their main weapon is about 0.0653

Hope this helped!