Will they be cured?

Probability Level pending

A new drug for hay fever is known to be successful in 40% of cases. Ten hay fever suffers take part in the testing of the drug.

What is the probability that exactly four people are cured? .

25% 36% 15% 16%

Lachlan Kuhr by Lachlan Kuhr , 22, Australia

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1 solution

Caleb Townsend
Mar 16, 2015

The probabilities that exactly 4 4 trials succeed out of 10 10 with a . 4 .4 success rate is ( 10 4 ) ( . 4 ) 4 ( 1 − . 4 ) 10 − 4 = 210 × . 0256 × . 046656 ≈ 0.25 \binom{10}{4}(.4)^4(1-.4)^{10-4} \\ = 210\times .0256\times .046656 \\ \approx \boxed{0.25}

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