Answer: 0.49668352
Step-by-step 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 : [tex]^nC_xp^x(1-p)^x[/tex]
The probability that at least two of the residents were unemployed :
[tex]P(x\geq2)=1-P(x<2)=1-(P(x=0)+P(x=1))[/tex]
[tex]1-(^8C_0(0.2)^0(0.8)^8+^8C_1(0.2)^1(0.8)^7)[/tex]
[tex]1-((1)(0.16777216)+(8)(0.2)(0.2097152))[/tex]
[tex]1-(0.16777216+0.33554432)[/tex]
[tex]1-(0.16777216+0.33554432)=1-0.50331648=0.49668352[/tex]
Hence, Required probability =0.49668352
