\begin{tabular}{l} There is a checkbox at the bottom of the exam form that you MusT check prior to submitting this exam. Failure to do so may cause your work to be lost. \ Question 1, multiple Choice Worth 2 points) \ (05.04 MC) \ Carson dives 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 so\% 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? \ $$ 14 \% $$ \ $$ 24 \% $$ \ \hline $$ 50 \% $$\end{tabular}

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UpStudy AI · Accepted Answer

To find the probability that Carson will not have to stop at either traffic light, we can follow these steps:

1. **Identify the probabilities of stopping at each light:**
   - Probability of stopping at the first light, $$ P(A) = 0.30 $$
   - Probability of stopping at the second light, $$ P(B) = 0.50 $$

2. **Calculate the probabilities of not stopping at each light:**
   - Probability of not stopping at the first light, $$ P(A') = 1 - P(A) = 1 - 0.30 = 0.70 $$
   - Probability of not stopping at the second light, $$ P(B') = 1 - P(B) = 1 - 0.50 = 0.50 $$

3. **Since the events are independent, the probability of not stopping at either light is the product of the individual probabilities:**
   $$
   P(A' \cap B') = P(A') \times P(B') = 0.70 \times 0.50
   $$

Now, let's calculate $$ 0.70 \times 0.50 $$:
Calculate the value by following steps:
- step0: Calculate:
  $$0.7\times 0.5$$
- step1: Multiply the numbers:
  $$0.35$$
The calculation gives us:

$$
0.70 \times 0.50 = 0.35
$$

This means the probability that Carson will not have to stop at either light is $$ 0.35 $$ or $$ 35\% $$.

Since this option is not listed in the choices provided, it appears there may be an error in the options given. The closest option to $$ 35\% $$ is not present, but the correct answer is $$ 35\% $$.
The probability that Carson will not have to stop at either light is $$ 35\% $$.

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