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A) what is the probability that the first contestant is a boy?



B) if the first contestant is a boy, what is the probability that the second contestant is a boy?


C) is the probability that the second contestant is a boy independent of the first contestant being a girl? Why?


Correct answer get BRAINLIEST!

Sagot :

MrRoyal

Probabilities are used to determine the chances of an event.

  • The probability that the first contestant is a boy is 1/2
  • The probability that the second contestant is a boy, if the first is a boy is 9/19
  • The probabilities are not independent

The given parameters are:

[tex]\mathbf{Contestants= 20}[/tex]

[tex]\mathbf{Girls= 10}[/tex]

[tex]\mathbf{Boys = 10}[/tex]

(a) Probability that first contestant is a boy

This is calculated as:

[tex]\mathbf{P(Boy) = \frac{Boys}{Contestants}}[/tex]

This gives

[tex]\mathbf{P(Boy) = \frac{10}{20}}[/tex]

[tex]\mathbf{P(Boy) = \frac{1}{2}}[/tex]

(b) Probability that the second contestant is a boy, if the first is a boy

This is calculated as:

[tex]\mathbf{P(Boy) = \frac{Boys - 1}{Contestants - 1}}[/tex]

We subtracted 1, because the first contestant (a boy) is no longer part of the selection.

So, we have:

[tex]\mathbf{P(Boy) = \frac{10-1}{20-1}}[/tex]

[tex]\mathbf{P(Boy) = \frac{9}{19}}[/tex]

(c) Independent probabilities

The probabilities are not independent, because when a contestant is selected, the number of contestant is reduced by 1.

And this will affect the probability of the next selection.

Read more about probabilities at:

https://brainly.com/question/11234923

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