Additional practice problems

Question

If a seed is planted, it has a 70% chance of growing into a healthy plant.

If 10 seeds are planted, what is the probability that exactly 2 don't grow?

Answer 1

P= 0.7 Q= 0.3

There are two outcomes, grow or not grow, so you recognize it is binomial.

We follow the formula for this

Use combination number, not permutation number, because the order doesn't matter. Combination number is N! / [(N-R)! R!]

10 = N, 2= R

Then we multiply this by .7^8 * .3^2

as .3 is chance that exactly those 2 don't grow, so we raise it to 2. While the rest, 8, still have a probability of .7 of growing.

Hope this helps!

Final answer should be .233

Answer 2

If a seed has a 70% chance of growing into a healthy plant, then it has a 30% chance of not growing.

The number x of plants that don't grow is a binomial variable, the probability that x = 2 can be found via the binomial probability formula:

C(10,2) (0.3)^2 (0.7)^8 = 0.233, where C(10,2) = 10!/(8!2!)