Question

If a seed is planted, it has a 60% chance of growing into a healthy plant. If 8 seeds are planted, what is the probability that exactly 4 don't grow?

Answer 1

Let x = number of seeds which do not grow

Given that ,

n = sample size = 8

Probability of seed grow = 0.60 and

Probability of seed not grow = 1 - 0.60 = 0.40

Here Let's define success to be seed does not grow  

i.e. P ( Seed does not grow ) = p = 0.40

we want to calculate the probability that exactly 4 seeds don't grow

By using Binomial distribution we can calculate it as

Binomial distribution has pdf

i.e.

  

.........................( ANSWER)

probability that exactly 4 don't grow = 0.2322