Question

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? 14% 24% 50% 80%

Explanation:

Step1: Find probability of not - stopping at first light

The probability of stopping at the first light is $P(S_1)=0.3$. So the probability of not - stopping at the first light is $P(\overline{S_1}) = 1 - 0.3=0.7$.

Step2: Find probability of not - stopping at second light

The probability of stopping at the second light is $P(S_2)=0.8$. So the probability of not - stopping at the second light is $P(\overline{S_2}) = 1 - 0.8 = 0.2$.

Step3: Use the multiplication rule for independent events

Since the two traffic lights are independent events, the probability of not stopping at either light is $P(\overline{S_1}\cap\overline{S_2})=P(\overline{S_1})\times P(\overline{S_2})$.
$P(\overline{S_1})\times P(\overline{S_2})=0.7\times0.2 = 0.14$ or $14\%$.

Answer:

14%