Question

If a seed is planted, it has a 95% chance of growing into a healthy plant. If 7 seeds are planted, what is the probability that exactly 2 don't grow

Answer 1

`(51998079)/(1280000000)` or around 0.0406

Explanation:

We need to choose 2 seeds that will not grow - there's

7 * 6 / 2 = 21 possibilities (choose one, chose second one, divide by 2 because each choice was counted twice).

The probability of each of those possibilities happening is:

`(5\%)^2 * (95\%)^5 = (2476099)/(1280000000)`

because two need to fail to grow and the rest need to grow properly.

The full probability is

`(51998079)/(1280000000)`