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Sagot :
Using the binomial distribution, the probabilities are given as follows:
- All: 0.2145 = 21.45%.
- None: 0.0013 = 0.13%.
- At least one: 0.9987 = 99.87%.
What is the binomial distribution formula?
The probability mass function for the binomial distribution is presented as follows:
[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 of the distribution are given by:
- n is the number of trials of the experiment.
- p is the probability of a success on a single trial of the experiment.
In the context of this problem, the values of these parameters are:
n = 5, p = 0.735.
The probability of all people ordering the breast sandwich is:
P(X = 5) = 0.735^5 = 0.2145 = 21.45%.
The probability of no people ordering the breast sandwich is:
P(X = 0) = (1 - 0.735)^5 = 0.0013 = 0.13%.
The probability of at least one person ordering the breast sandwich is:
P(X >= 1) = 1 - 0.0013 = 0.9987 = 99.87%.
More can be learned about the binomial distribution at https://brainly.com/question/24756209
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