SOLUTION: A man fires at a target six times; the probability of his hitting it each time is independent of other tries and is 0.40. (a) What is the probability that he will hit at least onc

Algebra ->  Probability-and-statistics -> SOLUTION: A man fires at a target six times; the probability of his hitting it each time is independent of other tries and is 0.40. (a) What is the probability that he will hit at least onc      Log On


   

Question 1177792: A man fires at a target six times; the probability of his hitting it each time is independent of other tries and is 0.40.
(a) What is the probability that he will hit at least once ?
(b) How many times must he fire at the target so that the probability of hitting it at least once is greater than 0.77 ?
(c) Interpret your findings.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
Binomial Distribution:  p (will hit target) = .40  
P+%28x%29=+highlight_green%28nCx%29%28p%5Ex%29%28q%29%5E%28n-x%29+ 
(a) n = 6:  P(at least once) = 1 - P(x = 0) = 1 - .0467 = .9533
  1 0r 2 0r 3 0r 4 0r 5 0r 6
.1866 + .31104 + .2765 + .1382 + .0369 + .0041 = .9533

(b) n = 3   P(at least once) = 1 - P(x ≤ 0) = 1 - .22 = .78

Wish You the Best in your Studies.