Answer to Question #330520 in Statistics and Probability for Natalia

Question

The latest nationwide political poll indicates that for Indians who

are randomly selected, the probability that they are with alliance

ABC is 0.55, the probability that they are with alliance PQR is

0.30 and the probability that they are with alliance XYZ is 0.15.

Answer the following questions pertaining to a randomly chosen

group of 10 Indians.

What is the probabilities:

(i) None are with alliance ABC ?

(ii) 2 are with alliance XYZ ?

(iii) At least 8 are with alliance PQR ?

Answer 1

1)$n=10, p=0.55, q=1-p=1-0.55=0.45$

$$P(Y=0)=\dbinom{10}{0}(0.55)^0(0.45)^{10-0}=$$ $$\approx0.000340506289$$

2)

$n=10, p=0.15, q=1-p=1-0.15=0.85$

$$P(W=2)=\dbinom{10}{2}(0.15)^2(0.85)^{10-2}=$$ $$\approx0.2758966566$$

3)

$n=10, p=0.3, q=1-p=1-0.3=0.7$

$$P(X\geq8)=P(X=8)+P(X=9)+P(X=10)$$ $$=\dbinom{10}{8}(0.3)^8(0.7)^{10-8}+\dbinom{10}{9}(0.3)^9(0.7)^{10-9}$$ $$+\dbinom{10}{10}(0.3)^10(0.7)^{10-10}=$$ $$=0.0015903864$$