The germination of cactus seeds is not easy. From experience, Lyla, an expert cactus grower, knows that on average, only 40% germinate. An intrepid collector returns from a very dry desert with six seeds of a previously unknown type of cactus.
Determine the most likely number of seeds to germinate (highest probability)
I know I can find the probability of each and then see which is highest. Is there a different way?
Best Answer
By the binomial distribution, (easy to find online) the probability that $k$ seeds generate is ${6 \choose k}(0.4)^k(1-0.4)^{6-k}$. The maximum will always occur either left or right of the expected value of the distribution, which is $6 \cdot 0.4 = 2.4$. So you just need to compute the binomial distribution probability values for $k=2$ and $k=3$ to find the maximum.