A commuter must pass through three traffic lights on her way to work. For each light, the probability that it is green when she arrives is 0.5. The lights are independent.
a) What is the probability that all three lights are green?
b) Let X be the number of times out of the five days in a given week that all three lights are green. Find P(X = 3).
a)
P(All three are green) = 0.5*0.5*0.5 = 0.125
b)
Here, n = 5, p = 0.125, (1 - p) = 0.875 and x = 3
As per binomial distribution formula P(X = x) = nCx * p^x * (1 -
p)^(n - x)
We need to calculate P(X = 3)
P(X = 3) = 5C3 * 0.125^3 * 0.875^2
P(X = 3) = 0.0150
A commuter must pass through three traffic lights on her way to work. For each light,...