Answer to Question #299306 in Statistics and Probability for Muss

Question

A meeting of consuls was attended by 4 Americans and 2 Germans. If three consuls were selected at random, construct the probability distribution of the random variable G representing the number of Germans

Answer 1

Americans: A = 4

Germans: G = 2

Total = 6

3 out of 6 can be selected in ⁶C₃ = 20 Ways

Germans can be 0 , 1 or 2

The number of Germans can not be 3 because they are only 2 in number.

three consuls were selected

G = 0  => ⁴C₃ x ²C₀ = 4 Ways

G = 1  => ⁴C₂ x ²C₁ = 12 Ways

G = 2  => ⁴C₁ x ²C₂ = 4 Ways 

G    P (G)          

0    ${4\over20} =0.2$  

1     ${12\over20} =0.6$      

2    ${4\over20} =0.2$