Question

A traffic control engineer reports that 75% of the vehicles passing through a checkpoint

are from within the state. What is the probability that fewer than 4 of the next 9 vehicles

are from out of state?

Answer 1

75% of the vehicles passing through a checkpoint are from within the state.

So, the probability that the vehicle is from within the state is 0.75.

The probability that the vehicle is from outside the state will be 1-0.75=0.25.

Now, let x be the random variable. So, the value of n=9. and x<4

It is required to calculate the probability that fewer than 4 of the next 9 vehicles are from out of state.

So, , p=0.25 and q=0.75.

So, the required probability can be calculated as,

Therefore, the probability that fewer than 4 of the next 9 vehicles are from out of state is 0.83427.