Answer: The probability that 3 or more belong to the ruling clique is 0.34.
Step-by-step explanation:
Since we have given that
Number of total members = 50
Number of belonging to ruling clique = 10
Number of belonging to second class member = 40
We need to find the probability that 3 or more belong to the ruling clique.
Let X be the number of outcomes belong to ruling clique.
So, it becomes,
P(X≥3)=1-P(X<3)
[tex]P(X\geq 3)=1-P(X=1)-P(X=2)\\\\P(X\geq 3)=1-\dfrac{^{10}C_1\times ^{40}C_5}{^{50}C_6}-\dfrac{^{10}C_2\times ^{40}C_4}{^{50}C_6}\\\\P(X\geq 3)=1-0.41-0.25\\\\P(X\geq 3)=0.34[/tex]
Hence, the probability that 3 or more belong to the ruling clique is 0.34.
