Question

According to a Department of Labor report, the city of Detroit had a 20% unemployment rate in May. Eight working-age residents were chosen at random. What is the probability that at least two of the residents were unemployed?

Answer 1

Answer: 0.49668352

Explanation:

Given : The unemployment rate : p = 20%= 0.20

Sample size : n =8

Let x be the binomial variable that represents the number of unemployed residents.

Binomial probability distribution formula :
`^nC_xp^x(1-p)^x`

The probability that at least two of the residents were unemployed :

`P(x\geq2)=1-P(x<2)=1-(P(x=0)+P(x=1))`

`1-(^8C_0(0.2)^0(0.8)^8+^8C_1(0.2)^1(0.8)^7)`

`1-((1)(0.16777216)+(8)(0.2)(0.2097152))`

`1-(0.16777216+0.33554432)`

`1-(0.16777216+0.33554432)=1-0.50331648=0.49668352`

Hence, Required probability =0.49668352