Alright, so it's official i'm not a math wiz. I'm currently trying to attempt a new unit, Probability. It's by far my worst section of matht and i have no clue how to start this problem.

In a biathlon, athletes shot at 20 targets. A particular athlete had a probability of 0.18 of missing a target. Assuming a binomial distribution, what is the probability, to the nearest thousandth, that the athlete hit exactly 16 targets?

Please teach me how to do this problem!!!! The decmal probability really throws me off. THANKS, erica

Hi Erica,

This is a problem on use of the formula for the binomial distribution. In your case n = 20 (number of trials), p = 0.18 (probability of succes in each trial) and k = 16 (number of succeses). So,

P(X=k) = C(n,k) p^k (1-p)^n-k, where C(n,k) are combinations n choose k (maybe you have a different notation). Hence P(X = 16) = C(20,16) 0.18¹⁶ (1 - 0.18)⁴.

Do these calculations.

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