MHB Probability Problem: At Least 1 Grow, At Least 1 Not Grow

[Yankel]

Hello all,

I am stuck with this one, it looks simple but yet confusing. Can you assist please ?

The probability of a flower to grow is 0.9. We put in the ground 4 seeds of this flower. What is the probability that at least
one will grow and at least one will not grow ?

Thank you.

 

[MarkFL]

We know:

It is certain that none will grow OR At least 1 will grow and 1 will not grow OR all will grow.

What are the probabilities that none will grow, and that all will grow?

 

[Yankel]

probability that all will grow is 0.6561 and that none will grow 0.0001, right ?

Now what ?

 

[MarkFL]

probability that all will grow is 0.6561 and that none will grow 0.0001, right ?

Now what ?

Yes, that's correct. :D

So now we want to take this:

It is certain that none will grow OR At least 1 will grow and 1 will not grow OR all will grow

and turn it into an equation. If we let $n$ be the number that grows we may write:

$$P(0)+P(1\le n\le3)+P(4)=1$$

You have already correctly determined $P(0)$ and $P(4)$, and so it is now just a matter of solving for $P(1\le n\le3)$, which is what we are trying to find. :)

 

[Yankel]

Oh...when you put it like this... :D

Thanks !