A motorist encounters four consecutive traffic lights, each equally likely to be red or green. Let be the number of green lights passed by the motorist before being stopped by a red light. What is the probability distribution of E?

P (X = 0) = 0.50          P (X = 3) = 0.0625

P (X = 1) = 0.25           P (X = 4) = 0.0625

P (X = 2) = 0.125

Step-by-step explanation:

The random variable E is denoted as the number of green lights passed by the motorist before being stopped by a red light.

Then the random variable E can take values, E = {0, 1, 2, 3, 4}

If X = 0, this implies that the motorists was stopped by the red light first.

         

If X = 1, this implies that the motorists passes 1 green light before being stopped by the red light.

         

If X = 2, this implies that the motorists passes 2 green lights before being stopped by the red light.

         

If X = 3, this implies that the motorists passes 3 green lights before being stopped by the red light.

       

If X = 4, this implies that the motorists passes 4 green lights before being stopped by the red light.

       

The probability distribution table for the random variable E attached below.