What is the probability the person is a clown, given they are a boy? (30 pts)

Question

contestada

Respuesta :

chisnau chisnau · Answer 1 · 2018-10-19T12:41:06+02:00

According to the table given:

Total number of students are = 20

Total number of boys are = 13 , out of which, 3 will be clowns, 2 will perform acrobats and 8 will be elephant trainers.

So, we have to find the the probability that the person(a boy) is a clown. The probability will be = [tex]\frac{3}{13}=0.230[/tex]

Hence, answer is 0.230

Answer Link

virtuematane virtuematane · Answer 2 · 2019-06-11T07:16:30+02:00

The probability the person is a clown, given they are a boy is:

0.23077

Let A denote the event that the person is a boy.

Let B denote the event that the person is a clown.

Then A∩B denote the event that the person is a boy and is a clown.

Let P denote the probability of an event.

Hence, from the table that is given to us we get:

P(A)=0.65

P(A∩B)=0.15

We are asked to find the probability the person is a clown, given they are a boy i.e. we are asked to find: P(B|A)

We know that:

[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}[/tex]

Hence, from the given values we have:

[tex]P(B|A)=\dfrac{0.15}{0.65}\\\\\\P(B|A)=\dfrac{15}{65}\\\\\\P(B|A)=\dfrac{3}{13}=0.23077[/tex]

Hence, the probability is:

0.23077