Question

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

Answer 1

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:

$\mathbf{Contestants= 20}$

$\mathbf{Girls= 10}$

$\mathbf{Boys = 10}$

(a) Probability that first contestant is a boy

This is calculated as:

$\mathbf{P(Boy) = \frac{Boys}{Contestants}}$

This gives

$\mathbf{P(Boy) = \frac{10}{20}}$

$\mathbf{P(Boy) = \frac{1}{2}}$

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

This is calculated as:

$\mathbf{P(Boy) = \frac{Boys - 1}{Contestants - 1}}$

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

So, we have:

$\mathbf{P(Boy) = \frac{10-1}{20-1}}$

$\mathbf{P(Boy) = \frac{9}{19}}$

(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:

brainly.com/question/11234923