Respuesta :
Option b is correct. The probability that you and your friend are both chose is 4/20.
What is probability?
The probability provides a means of getting an idea of likelihood of occurrence of different events resulting from a random experiment in terms of quantitative measures ranging between zero and one.
Formula for probability
P(E) = number of favorable outcomes/Total number of outcomes
Where,
P(E) is the probability of an event.
What is combination?
An arrangement of objects where the order in which the objects are selected does not matter is called combination.
Combination Formula
[tex]C_{n,k} = \frac{n!}{(n-k)!k!}[/tex]
Where,
n is total number of objects in set
[tex]C_{n, k}[/tex] is number of combinations
k is number of choosing objects from the set
According to the given question
We have
Total six people.
And,
There are total [tex]6C_{3}[/tex] ways to choose the 3 contestants.
⇒ [tex]6C_{3} = \frac{6!}{(6-3)!3!}[/tex] = [tex]\frac{(6)(5)(4)(3!)}{(3!)(3!)}[/tex] = 20
⇒ total number of outcomes = 60
⇒ There are 20 ways to select 3 contestant among 20 people.
Now, the number of ways that, you and your friend are chosen, along with 1 person from a set of 4 is given by
[tex]C_{4,1} = \frac{4!}{1!3!}= 4[/tex]
⇒ total number of favorable outcomes = 4
Therefore,
The probability that you and your friend are both chose = [tex]\frac{4}{20}[/tex]
Hence, option b is correct.
Learn more about probability and combination here:
https://brainly.com/question/11234257
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