Question

There are 20 children in the cast of a class play, and 8 of the children are boys. Of the boys, 4 have a speaking part in the play, and of the girls, 8

do not have a speaking part in the play. If a child from the cast of the play is chosen at random, what is the probability that the child has a
speaking part?
A: 2/5
B: 1/2
C: 3/5
D: 3/4

Answer 1

A 2/5 of the students because because 8 out of the 20 students have speaking parts

Answer 2

Taking into account the definition of probability, the correct option is option A.: The probability that the child has a speaking part is
`(2)/(5)`.

There are 20 children in the cast of a class play, and 8 of the children are boys. Then, realizing the difference between the number of children and the number of boys you get that 12 of the children are girls.

On the other side, of the boys, 4 have a speaking part in the play, and of the girls, 8 do not have a speaking part in the play. Then, calculating the difference between the number of girls there are and the number of them that they do not have a speaking part in the play is obtained: 12 girls - 8= 4 girls. So, of the girls, 4 do not have a speaking part in the play.

Therefore, 4 + 4 = 8 of the children have a speaking part.

Probability is the greater or lesser possibility of a certain event occurring. In other words, probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

`P(A)=(number of favorable cases)/(number of possible cases)`

In this case:

• number of favorable cases= 8 of the children have a speaking part.
• number of possible cases= 20 children

Replacing in the definition of probability:

`P(A)= (8)/(20)`

Simplifying the fraction:

`P(A)= (2)/(5)`

Then, the correct option is option A.: The probability that the child has a speaking part is
`(2)/(5)`.