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ANTONII [103]
3 years ago
7

Help binomial distributions

Mathematics
1 answer:
Ymorist [56]3 years ago
3 0

We have the formula to compute the probability of having exactly k successed over n trials, given a probability p of success (and implicitly a probability 1-p of failure), which is


P(\text{k successed on n trials}) = \binom{n}{k}p^k(1-p)^{n-k}


Now, the probability of at least 3 successes is the union of the following event: exactly three successes,exactly four successes and exactly five successes.


We can compute their probability and sum them:\binom{5}{3}\left(\frac{3}{7}\right)^3\left(\frac{4}{7}\right)^2 + \binom{5}{4}\left(\frac{3}{7}\right)^4\left(\frac{4}{7}\right)^1 + \binom{5}{5}\left(\frac{3}{7}\right)^5 \approx 0.36788


So, the answer is about 36.79%

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