SOLUTION: The city finds empirically that the probability that an automobile going through the intersection of 5th and Main will run a red light sometime during a given day is 9.3%, and the

Algebra ->  Probability-and-statistics -> SOLUTION: The city finds empirically that the probability that an automobile going through the intersection of 5th and Main will run a red light sometime during a given day is 9.3%, and the       Log On


   

Question 1129841: The city finds empirically that the probability that an automobile going through the intersection of 5th and Main will run a red light sometime during a given day is 9.3%, and the probability that an automobile going through the intersection of 7th and Polk will run a red light sometime during a given day is 11.7%. Suppose a car is picked at random at 5th and Main on a given day and another at random at 7th and Polk. Write each probability as a percentage rounded to one decimal place.
What is the probability that neither car runs a red light?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Let's call the two cars: car A, car B

Car A has a 9.3% chance of running the red light (intersection of 5th and main) so it has a 100-9.3 = 90.7% chance it does not run a red light.

Car B has a 11.7% of running the red light (intersection 7th and polk) meaning it has a 100-11.7 = 88.3% chance of not running the red light.

Convert each percentage to decimal form
90.7% ---> 0.907
88.3% ---> 0.883

Now multiply those decimal values:
0.907*0.883 = 0.800881
this multiplication works because the two events are independent

Convert the result to percent form
0.800881 ---> 80.0881%
which rounds to 80.1%

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Answer: 80.1%
This is the probability that both cars together do not run their respective red lights.