Question

3. A meeting of consuls was attended by 4 Americans and 2 Germans. If three
consuls were selected at random one after the other, determine the values of
the random variable G representing the number of Germans.​

Answer 1

Given : A meeting of consuls was attended by 4 Americans and 2 Germans.

three  consuls were selected at random one after the other,

To Find : determine the values of the random variable G representing the number of Germans.​

Solution:

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

three consuls were selected

G =  0     =>   ⁴C₃*²G₀  = 4  Ways

G =  1     =>   ⁴C₂*²G₁  = 12  Ways

G =  2     =>   ⁴C₁*²G₂  = 4  Ways  

G         P (G)                       G. P(G)

0         4/20 =0.2                 0

1          12/20 =0.6               0.6

2        4/20 =0.2                 0.4

Expected Value =   ∑  G. P(G)

= 0 + 0.6 + 0.4

= 1

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