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Sagot :
Answer:
[tex]0.19[/tex]
Step-by-step explanation:
For exactly [tex]1[/tex] person to get yes, let's first count the probability of getting a yes on [tex]a[/tex] or [tex]b[/tex]. The chance of getting a yes on a is [tex]0.10[/tex], and likewise for [tex]b[/tex]. So, the answer is [tex]0.10+0.10=0.20=0.2[/tex], right?
Wrong! We overcounted the possibility that both [tex]a[/tex] and [tex]b[/tex] get a yes. We need to subtract the possibility [tex]a[/tex] gets a yes times the possibility [tex]b[/tex] gets a yes from [tex]0.2[/tex].
We get [tex]0.2-(0.1)(0.1)=0.2-0.01=0.19[/tex].
So, the answer is [tex]0.19[/tex] and we're done!
Using the binomial distribution, it is found that there is a 0.18 = 18% probability of getting exactly one yes.
For each call, there are only two possible outcomes, either it is a yes or it is a no. The output of each call is independent of other calls, 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:
- The chance of getting a yes on a telemarketing call is 0.10, hence p = 0.1.
- Two calls are made, hence n = 2.
The probability of getting exactly one yes is P(X = 1), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{2,1}.(0.1)^{1}.(0.9)^{1} = 0.18[/tex]
0.18 = 18% probability of getting exactly one yes.
You can learn more about the binomial distribution at https://brainly.com/question/24863377
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