Question

A commuter must pass through five traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits (x), as shown below:

x	0	1	2	3	4	5
p(x)	0.03	0.21	p	0.1	0.1	0.05

Find the probability that she hits at most 3 red lights. Answer to 2 decimal places.

Tries 0/5

Find the probability that she hits at least 3 red lights. Answer to 2 decimal places.

Tries 0/5

How many red lights she expect to hit? Answer to 2 decimal places.

Tries 0/5

What is the standard deviation of number of red lights she hits? Answer to 3 decimal places.

Tries 0/5

Let us consider any two consecutive days. What is the chance that she hits exactly two red lights on both days? Answer to 4 decimal places.

Answer 1

The Table given

x	0	1	2	3	4	5
p(x)	0.03	0.21	p	0.1	0.1	0.05

We know for probability function  

Therefore ,

Probability that she hits at most 3 red lights

Probability that she hits at most 3 red lights is 0.85

Probability that she hits atleast 3 red lights

Probability that she hits atleast 3 red lights is 0.25

Number of red lights she expect to hit

Red lights she expect to hit is 2.18

Standard deviation

Standard deviation of number of red lights she hits is 1.117

Probability she hits excatly two red lights on both days

The chance that she hits excatly two red lights on both days is 0.2601