Question

A school class went on a field trip to see a magician perform there were 17 females 20 males in the class the magicians randomly selected a volunteer from the audience in which had 52 females and 68 males given that the randomly selected audience member is a student from the class which equation can be used to find the probability p that the perdimos also a female?please help does anyone know the answer

Answer 1

Answer:

P(B)= 17/20

Step-by-step explanation:

Hello!

The audience of the magic show is conformed by a total of 120 people, 52 of which are female and 68 are men.

Within the audience there is a school class of 37, of these students, 17 are female and 20 are male.

If a random member of the audience is selected as a volunteer:

Let "A" represent the event that "the selected volunteer is a student of the class"

And "B" the event that "the selected student is female"

You have to calculate the probability of the selected volunteer being female, given that it is a member of the school class.

Symbolically:

P(B|A)

Using the formula of conditional probabilities you can calculate it as:

$P(B|A)= \frac{P(AnB)}{P(A)}$

P(A∩B)= $P(A)*P(B)= (\frac{37}{120} )*(\frac{17}{20} )$= $\frac{629}{2400}= 0.26$

$P(A)= \frac{37}{120} = 0.308$

$P(B|A)= \frac{P(AnB)}{P(A)}= \frac{629/2400}{37/120} = \frac{17}{20} = 0.85$

As you can see the probability of the event "The volunteer is female given that it was a student of the school class" means that you already know the selected volunteer was a student and only needed to calculate the probability of that student being female.

P(B)= 17/20

I hope this helps!