Respuesta :
Answer:
Step-by-step explanation:
When A, B,C are equally likely to be assigned to any one of the stations 1,2 or 3
we find that each one assigned to one station has probability 1/3
Also each person is independent of the other.
Probability that
a) All three family members are assigned to the same station
= P(ABC) to same station
= P(ABC) to 1+P(ABC) to 2 +P(ABC) to 3
=3*P(A)P(B)P(C) since independent
=[tex]3*(\frac{1}{3} )^3\\=\frac{1}{9}[/tex]
b) This would be equivalent to 1- all 3 to the same station
= [tex]1-\frac{1}{9} \\=\frac{8}{9}[/tex]
c) Every member to a different station
A has 3 choices while B has remaining 2 and C has 1
Hence prob = [tex]\frac{3*2*1}{3*3*3} =\frac{2}{9}[/tex]
The probability that three family members are assigned to the same station is 1/9.
How to calculate the probability?
From the information given, the probability that all three family members are assigned to the same station will be:
= 3 × (1/3)³
= 1/9
The probability that at most two family members are assigned to the same station will be:
= 1 - 1/9
= 8/9.
Lastly, the probability that every family member is assigned to a different station will be:
= 1 × 2/3 × 1/3
= 2/9
Learn more about probability on:
https://brainly.com/question/25870256
