Question

4, A faculty member submits 6 proposals in a year. They have a 21% probability of securing an NSF grant (a grant' means a funded proposal) every time they submit an unsolicited proposal, assuming that the number of proposals submitted has no effect on the probability of funding, and assuming that each proposal is reviewed independently. Find the probability that the professor secures 2 grants after submitting only 3 proposals

Answer 1

Probability of securing a NSF grant, p = 0.21

q = 1-p = 1-0.21 = 0.79

Number of grant submitted, n= 3

Probability that the professor secures 2 grants after submitting 3 proposals, P(X=2) =

$\\ \\ =\ ^{3}C_2*p^2*q^1 \\ \\ =\ \frac{3!}{2!*1!}*0.21^2*0.79^1 = \textbf{0.104517}$