prob that a planted seed will sprout is 3/4; if I plant 7, what is prob that at least 5 will sprout?

Question

It is a probability question based on events are independent or mutually exclusiive.

Answer 1

Either a planted seed will sprout (p=¾) or it won't sprout (q=¼) so we could use the binomial expansion (p+q)⁷ to find all possibilities.

(p+q)⁷=1=p⁷+7p⁶q+[(7)(6)/2!]p⁵q²+...

[(7)(6)/2!]p⁵q²=21p⁵q² (probability that 5 seeds will sprout) = 21×¾⁵×¼²=21×3⁵/4⁷=21×243/16384=5103/16384=0.31 approx or about 31%.