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Sagot :
Answer:
0.6889 = 68.89% probability that a customer likes this flavor the first time and the second time
Step-by-step explanation:
For each time the customer is asked, there are only two possible outcomes. Either they like the flavor, or they do not. Each event is independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The probability that a customer likes the new flavor is .83.
This means that [tex]p = 0.83[/tex]
What is the probability that a customer likes this flavor the first time and the second time
This is P(X = 2) when n = 2. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,2}.(0.83)^{2}.(0.17)^{0} = 0.6889[/tex]
0.6889 = 68.89% probability that a customer likes this flavor the first time and the second time
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