SOLUTION: The probability of being a smoker among a group of cases with lung cancer is 0.75. Calculate the probability that in a group of 6 cases, you have at least 3 smokers.

Algebra ->  Probability-and-statistics -> SOLUTION: The probability of being a smoker among a group of cases with lung cancer is 0.75. Calculate the probability that in a group of 6 cases, you have at least 3 smokers.      Log On


   

Question 1165286: The probability of being a smoker among a group of cases with lung cancer is
0.75. Calculate the probability that in a group of 6 cases, you have at least 3
smokers.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

One less calculation to compute this as 1-Pr(2 or fewer smokers)

Probability of nonsmoker is 1-0.75 = 0.25

Probability of at least 3 smokers = 1 - (probability of 2 or fewer smokers)

Probability of 0 smokers: +0.25%5E6+=+0.0002441+
Probability of 1 smoker : +0.25%5E5+%2A+0.75%5E1+%2A+6C1+=+0.0043945+
Probability of 2 smokers: +0.25%5E4+%2A+0.75%5E2+%2A+6C2+=+0.0329590+


Sum is 0.037598


Proability of at least 3 smokers = 1-0.037598 = +highlight%28+0.96240+%29+


You can try solving it in a direct method (pr(3)+pr(4)+pr(5)+pr(6) smokers) to prove to yourself that the answer comes out the same.