If a seed is planted, it has a 95% chance of growing into a healthy plant. If 6 seeds are planted, what is the probability that exactly 3 don't grow?

Question

If a seed is planted, it has a 95% chance of growing into a healthy plant.

If 6 seeds are planted, what is the probability that exactly 3 don't grow?

Answer 1

The probability that a plant will not grow to a health plant is 5%

So

the probability that 3 plant do not grow is ₆C₃p³q³ = 6!/(3!(6-3)!)(.05)³(.95)³ = .00214

Strangely, the probability that only 3 plants will grow is ₆C₃(.95)³(.05)³ = .00214 !