probability of growing a healthy plant

• Aug 2nd 2009, 06:25 PM
skorpiox
probability of growing a healthy plant
If a seed is planted, it has a 65% chance of growing into a healthy plant.

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

I subtracted 1 from the probability that exaxtly 2 will grow , and my anwser is 1-.0042813781= 0.99572 ; is this correct , or do I have to do something else . Thanks in advance!!
• Aug 2nd 2009, 06:37 PM
Chris L T521
Quote:

Originally Posted by skorpiox
If a seed is planted, it has a 65% chance of growing into a healthy plant.

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

I subtracted 1 from the probability that exaxtly 2 will grow , and my anwser is 0.99572; is this correct , or do I have to do something else . Thanks in advance!!

Note that if X represents the number of plants that grow, then it follows that $\displaystyle X$ has a $\displaystyle \mathcal{B}\left(10,.65\right)$ distribution.

If we want to know the probability of exactly two plants failing to grow, its the same as asking for the probability of exactly eight plants that succeeded to grow.

So it follows that the answer is $\displaystyle P\left(X=8\right)={10\choose 8}\left(.65\right)^{10}\left(.35\right)^{10-8}\approx0.0742$

Does this make sense?
• Aug 2nd 2009, 06:51 PM
artvandalay11
This is a binomial distribution problem with n=10, p=.65

We want to know the probability that 8 plants grow, so k=8

$\displaystyle P(k)={{n}\choose{k}}p^k(1-p)^{n-k}$

$\displaystyle P(8)={{10}\choose{8}}(.65)^8(1-.65)^{10-8}$

$\displaystyle {{n}\choose{k}}$ is notation for nCr in case you didnt know and you should be good from here
• Aug 2nd 2009, 07:12 PM
skorpiox
thank you guys ; I got it. I guess I was thinking about normal distribution