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

  • MHB
  • Thread starter Yankel
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In summary, the conversation involves a discussion about the probability of a flower growing, with the given information that the probability is 0.9 and that 4 seeds have been planted. The conversation also includes the probabilities of none or all of the seeds growing, as well as an equation to solve for the probability of at least one seed growing and at least one not growing. The conversation concludes with a thank you and an expression of understanding.
  • #1
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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  • #2
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?
 
  • #3
probability that all will grow is 0.6561 and that none will grow 0.0001, right ?

Now what ?
 
  • #4
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:

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

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. :)
 
  • #5
Oh...when you put it like this... :D

Thanks !
 

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

What is the probability that at least one plant will grow and at least one plant will not grow?

The probability of at least one plant growing and at least one plant not growing depends on the specific situation and the probabilities assigned to each outcome. It is important to note that the sum of the probabilities of all possible outcomes must add up to 1.

How do you calculate the probability of at least one plant growing and at least one plant not growing?

To calculate the probability of at least one plant growing and at least one plant not growing, you can use the formula P(A or B) = P(A) + P(B) - P(A and B), where A represents the event of at least one plant growing and B represents the event of at least one plant not growing. P(A and B) represents the probability of both events occurring simultaneously.

Can the probability of at least one plant growing and at least one plant not growing be greater than 1?

No, the probability of any event cannot be greater than 1. A probability of 1 represents a certain outcome, while a probability of 0 represents an impossible outcome. The sum of the probabilities of all possible outcomes must always equal 1.

How does the number of plants affect the probability of at least one plant growing and at least one plant not growing?

The number of plants can affect the probability of at least one plant growing and at least one plant not growing. As the number of plants increases, the probability of at least one plant growing also increases. However, the probability of at least one plant not growing decreases as the number of plants increases.

What other factors can affect the probability of at least one plant growing and at least one plant not growing?

Other factors that can affect the probability of at least one plant growing and at least one plant not growing include environmental conditions, such as sunlight and water availability, and the health of the plants. These factors can increase or decrease the likelihood of a plant growing or not growing.

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