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 2 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

a)

Here, n = 4, p = 0.5, (1 - p) = 0.5 and x = 1
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 1)
P(X = 1) = 4C1 * 0.5^1 * 0.5^3
P(X = 1) = 0.25

b)

Here, n = 8, p = 0.5, (1 - p) = 0.5 and x = 2
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 2)
P(X = 2) = 8C2 * 0.5^2 * 0.5^6
P(X = 2) = 0.1094