Question

(1 point) A sign on the pumps at a gas station encourages customers to have their oil checked, and claims that one out of 5 cars needs to have oil added. If this is true (and assuming cars arriving independently), find the probability of each of the following: A. Exactly 1 of the next 4 cars needs oil. Probability = B. Exactly 2 of the next 8 cars needs oil. Probability =

Answer 1

X ~ Bin(n,p)

Where p = 1/5 = 0.20

P(X) = ⁿC_x * p^x * ( 1 - p)^n-x

a)

For n = 4,

P(X = 1) = ⁴C₁ * 0.20¹ * ( 1 - 20)^4-1

= 0.4096

b)

For n = 8,

P(X = 2) = ⁸C₂ * 0.20² * ( 1 - 20)^8-2

= 0.0011