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

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The probability of a flower growing from a seed is 0.9, and four seeds are planted. The probabilities that all seeds grow is calculated as 0.6561, while the probability that none grow is 0.0001. To find the probability that at least one seed grows and at least one does not, the equation P(0) + P(1 ≤ n ≤ 3) + P(4) = 1 is established. With P(0) and P(4) known, the next step is to solve for P(1 ≤ n ≤ 3). This approach clarifies the problem and leads to the desired probability calculation.
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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.
 
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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?
 
probability that all will grow is 0.6561 and that none will grow 0.0001, right ?

Now what ?
 
Yankel said:
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. :)
 
Oh...when you put it like this... :D

Thanks !
 
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