Respuesta :
Answer:
The probability that conservative party wins all 3 seats is 0.216
The probability that conservative party wins exactly two seats is 0.432
Step-by-step explanation:
Consider the provided information.
The probability of a conservative candidate winning is p=0.6.
The probability of one progressive candidate will win is: 1-0.6=0.4
Part (a) What is the probability that the conservative party wins all three seats?
According to binomial distribution: [tex]b(x; n, p) =^nC_xp^x(1- p)^{n-x}[/tex]
[tex]P(x=3) =^3C_3(0.6)^3 (0.4)^{3-3}[/tex]
[tex]P(x=3) =(0.6)^3[/tex]
[tex]P(x=3)=0.216[/tex]
P(conservative party wins all 3 seats) = 0.216
Hence, the probability that conservative party wins all 3 seats is 0.216
Part (a) What is the probability that the conservative party wins exactly two seats?
[tex]P(x=2) =^3C_2(0.6)^2 (0.4)^{3-2}[/tex]
[tex]P(x=2) =3(0.36)(0.4)[/tex]
[tex]P(x=2) =0.432[/tex]
Hence, the probability that conservative party wins exactly two seats is 0.432
