Question

A tree has a 25% chance of flowering. In a random sample of 15 trees, what is the probability that at least 4 develop flowers?

Answer 1

I would calculate this: 1 - p(0) - p(1) - p(2) - p(3).

Answer 2

I wouldn't do P(4) + P(5) + ... P(15)

:DD

Answer 3

Presumably we are getting P(n) from the binomial distribution.

Answer 4

\(\color{blue}{\text{Originally Posted by}}\) @SithsAndGiggles
The probabilities themselves are binomial. If \(P(X=k)\) denotes the probability that \(k\) flowers develop, then
\[P(X\ge4)=1-P(X<4)=1-\bigg(\color{red}{P(X=0)}+P(X=1)+P(X=2)+P(X=3)\bigg)\]
as mentioned above.

\[P(X=k)=\dbinom{15}k(0.25)^k(1-0.25)^{15-k}\]
\(\color{blue}{\text{End of Quote}}\)