Using the binomial distribution, it is found that there is a 0.875 = 87.5% probability that at least one of your next three seeds sprout.
For each seed, there are only two possible outcomes, either it sprouts, or it does not. The probability of a seed sprouting is independent of any other seed, hence the binomial distribution is used to solve this question.
What is the binomial distribution formula?
The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- 50% of seeds sprout, hence p = 0.5.
- There are 3 seeds, hence n = 3.
The probability that at least one of your next three seeds sprouts is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.5)^{0}.(0.5)^{3} = 0.125[/tex]
Then:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.125 = 0.875[/tex]
0.875 = 87.5% probability that at least one of your next three seeds sprout.
More can be learned about the binomial distribution at https://brainly.com/question/14424710
