Question

3.61 In 2000 the population of California consisted of approximately 80% white, 8% black, and 12% Asian. Perform the following calculations. a. Find the probability that you met 3 white individuals, 1 black individual, and 1 Asian individual if you randomly met 5 Californians in 2000. b. Find the probability that you met more white people than black and Asian people combined if you randomly met 5 Californians in 2000.

Answer 1

Explanation:

Given that in 2000 the population of California consisted of approximately 80% white, 8% black, and 12% Asian.

Individuals met = 5

a) probability that you met 3 white individuals, 1 black individual, and 1 Asian individual if you randomly met 5 Californians in 2000.

=favourable outcomes/total outcomes =
`0.8^3(0.08)(0.12)\\= 0.0049152`

b) the probability that you met more white people than black and Asian people combined if you randomly met 5 Californians in 2000.

(w,nonwhite) = (3,2) or (4,1) Or (5,0)

Or (w,b,a) = (2,1,2) or (2,0,3) or (1,0,4) or (3,1,1) or (3,2,0) or (3,0,2) or (4,0,1) or (4,1,0) or (5,0,0)

Hence prob
`= 0.8^2[(0.08)(0.12)^2+(0.12)^3]+0.8(0.12)^4 +(0.8)^3[0.08(0.12)+0.08^2+0.12^2] +(0.8)^4[(0.12) + 0.08]+0.8^5`