Question

A well-traveled highway has its traffic lights green for 82% of the time. If a person traveling the
road goes through 8 traffic intersections, complete the chart to find a) the probability that the first
red light occur on the nth traffic light and b) the cumulative probability that the person will hit the
red light on or before the nth traffic light.
Also, find the expected number of traffic lights to hit a red light and the probability that you will go through
more than 8 lights before seeing your first red light

Answer 1

what i know is it is geometric distribution but how to calculate its cummulative ? and the last part

Answer 2

can you draw the geometric distribution...?

Answer 3

by draw u mean ?

Answer 4

yeah

Answer 5

i have solved the first part by the formula pq^(x-1), where p is 0.18 q is 0.82 and xis 8 and the answer was 0.045 i did the cummulative part by summing all the value from 1 to 8 and the answer was 0.796. the expected value i calculated by the formula 1/p was 5.56 but i am stuck at the next part and i don't know if the answers are correct.

Answer 6

good... let em explain the other parts...

Answer 7

ok. btw are the answers correct ? have i calculated them correctly ?

Answer 8

***the first part by the formula pq^(x-1), where p is 0.18 q is 0.82 and xis 8 and the answer was 0.045... it's correct

Answer 9

the second one is also correct... .0.796

Answer 10

the probability that you will go through more than 8 lights before seeing your first red light - i am stuck at this part :/

Answer 11

the probability that you will go through more than 8 lights before seeing your first red light is (1-0.18)^8 = 0.204

Answer 12

how ? can you please explain ?

Answer 13

(n-p)^n

Answer 14

i haven't been taught this formula yet .. either can u state another method or explain the logic behind it ?

Answer 15

it's the formula of the cumulative probability

Answer 16

but they haven't used the word cumulative so how are we going to identify ?

Answer 17

look at ur question....


b) the cumulative probability

Answer 18

i have solved that already and the answer was 0.796 but i can't solve this

"the probability that you will go through more than 8 lights before seeing your first red light"

Answer 19

so the expected number of traffic lights to hit a red light and the probability that you will go through more than 8 lights before seeing your first red light can be solved by such method...

Answer 20

can u elaborate a little more ?

Answer 21

i am now confused with your comments....

Answer 22

i can't get this formula because c.d.f formula is to simple add all the values a/c to condition
for e.g. in part b) i added all the value from 1 to 8 and got 0.7936 so how come the formula change over here ? and how to identify when to use that formula ? plus what's the logic behind it

Answer 23

@ganeshie8 please have a look sir....

Answer 24

No idea sorry...

Answer 25

@hartnn please have a look here... need ur help...

Answer 26

@tkhunny please help here...