Probability practice problem

Question

If a seed is planted, it has 85% chance in growing. If 8 seeds are planted, what is the probability that exactly 2 don’t grow

Answer 1

This problem seeks to confuse by giving the probability of growing and the number not growing. The 2 values need to be consistent - either change the probability of growing to probability not growing or change number not growing to number growing.

p = .85 and 2 are not growing; there are 8 plants (n = 8)

If we choose to change to the the number growing, p = .85 and x = n - 2 = 8 - 2 = 6

To get the probability growing, we can either use the binomial distribution formula,

P(x) = C(n,x)p^x(1-p)^n=x = C(8,6).85⁶.15² = 28 * .37715 * .0225 = .2376

or let Excel/our calculator do the work by providing n, x, and p

In Excel, we use = binom.dist(6,8,.85,0) and get the same answer

the 0 at the end tells us that we want the probability of exactly 6, not the number <= 6.