Answer:
Expected Value = 0.9206
so expected value we expect 1 liberal to be chose
Step-by-step explanation:
given data
delegation = 3 selected
liberals = 4
conservatives = 5
solution
we know that Delegates total 4 liberals 5 conservatives.
so here Probability of getting a liberal is
Probability of getting a liberal = [tex]\frac{4}{9}[/tex]
and
Expected Value will be here
Expected Value = [tex]\frac{4}{9}1 + \frac{4}{9} \frac{3}{8} +\frac{4}{9} \frac{3}{8} \frac{2}{7}[/tex] 3
Expected Value = 0.4444 + 0.3333 + 0.1428
Expected Value = 0.9206
so expected value we expect 1 liberal to be chose
The expected number of liberals in the delegation is 1
The given parameters are:
Liberals = 4
Conservatives = 5
So, the probability of a liberal is:
[tex]p = \frac{4}{4 + 5}[/tex]
Evaluate the sum
[tex]p = \frac{4}{9}[/tex]
The delegation is made of 3 council members.
So, the expected number of liberal is calculated as:
[tex]\bar x =np[/tex]
This gives
[tex]\bar x = 3 * \frac 49[/tex]
Evaluate
[tex]\bar x = 1.33[/tex]
Approximate
[tex]\bar x = 1[/tex]
Hence, the expected number of liberals in the delegation is 1
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