Respuesta :
The probability of getting a vowel on exactly 3 of the spins when the spinner is spin 5 number of times is 0.1646.
What is binomial probabilities?
The binomial probabilities is the experimental probability in which the total number of output values is 2, therefore it is known as binomial probabilities.
The number of independence variable in case of binomial experiments is fixed. Both the two output has the 1/2 chances to occur.
It can be given by the function,
[tex]P(X)=\left(^nC_x\right)p^x(1-p)^{n-x}[/tex]
Here, (n) is the number of trial (x) is a number of successes desired and (p) is the probability of success in one trial.
The spinner has 3 sections, let A,B and C, in which A one is vowel. Hence, the probability of getting vowel in one spin is,
[tex]p=\dfrac{1}{3}\\p=0.333[/tex]
It spins the spinner 5 times. Thus,
[tex]n=5[/tex]
The probability of of getting a vowel on exactly 3 of the spins is,
[tex]P(X=3)=\left(^5C_3\right)0.333^3(1-0.333)^{5-3}\\P(X=3)=0.1646[/tex]
Thus, the probability of getting a vowel on exactly 3 of the spins when the spinner is spin 5 number of times is 0.1646.
Learn more about the binomial probability here;
https://brainly.com/question/24756209
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