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

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Discussion Overview

The discussion revolves around a probability problem involving the growth of flower seeds. Participants explore the probability that at least one seed will grow and at least one will not grow, given a specific probability of growth for each seed. The scope includes mathematical reasoning and problem-solving related to probability theory.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant presents the problem of determining the probability that at least one seed will grow and at least one will not grow, given a growth probability of 0.9 for each of the four seeds.
  • Another participant outlines the possible outcomes: none will grow, at least one will grow and one will not, or all will grow.
  • There are calculations presented for the probabilities of all seeds growing (0.6561) and none growing (0.0001), with a request for confirmation of these values.
  • A later reply confirms the calculations for the probabilities of all and none growing, and suggests a method to express the problem in terms of an equation involving the probabilities.
  • Participants express a sense of clarity and appreciation for the structured approach to solving the problem.

Areas of Agreement / Disagreement

Participants generally agree on the calculations for the probabilities of all and none of the seeds growing, but the overall problem remains unresolved as they work towards finding the probability of at least one growing and one not growing.

Contextual Notes

There are unresolved steps in deriving the probability of at least one seed growing and one not growing, as well as dependencies on the assumptions made regarding the independence of seed growth.

Yankel
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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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