Carson drives to school the same way each day, and there are two independent traffic lights on his trip to school. He knows that there is a 30% chance that he will have to stop at the first light and an 80% chance that he will have to stop at the second light. What is the probability that he will NOT have to stop at either light?
A) 14%
B) 24%
C) 50%
D) 80%
I think the answer is C) 50%
How did you come up with 50%?
To find the probability that Carson will NOT have to stop at either light, we need to find the complement of the events where he stops at each light.
The probability that he will have to stop at the first light is given as 30%, which means the probability of not stopping at the first light is 100% - 30% = 70%.
Similarly, the probability that he will have to stop at the second light is given as 80%, which means the probability of not stopping at the second light is 100% - 80% = 20%.
Since the two lights are independent events, we can multiply the probabilities of not stopping at each light to find the overall probability of not stopping at either light.
Probability of not stopping at both lights = Probability of not stopping at first light * Probability of not stopping at second light
= 70% * 20%
= 14%
Therefore, the probability that Carson will NOT have to stop at either light is 14%.
Hence, the correct answer is A) 14%.
I am not exactly sure but... Since there is a 30% chance that he will have to stop at the first light, there is a 70% chance that he won't. And since there is an 80% chance he will have to stop at the second light, there is a 20% chance he won't.
So I subtracted -> 70% - 20% = 50%
If there is a 70% chance he won't have to stop at the first light, and a 20% chance he won't have to stop at the second light, then there is a 50% chance he won't have stop at either light.
(By the way, have you learned how to solve these types of probability problems already?)