Ms. tucker travels through two intersections with traffic lights as she drives to the market. the traffic lights operate independently. the probability that both lights will be red when she reaches them is 0.22. the probability that the first light will be red and the second light will not be red is 0.33. what is the probability that the second light will be red when she reaches it?

The probability that the second light will be red when she reaches it is .

Step-by-step explanation:

Given: Ms. tucker travels through two intersections with traffic lights as she drives to the market. the traffic lights operate independently. the probability that both lights will be red when she reaches them is . the probability that the first light will be red and the second light will not be red is .

According to question:

The probability of two independent events occurring one after the another is the product of these probabilities written as .

We have given that the probability of the first being red and the second not being red is .

The probability of the first light being red is .  

And we know that these events are independent, then

Therefore, probability that the second light will be red when she reaches it is .

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The probability that the second light will be red when she reaches it is;

P(R₂) = 0.4

We are given;

Probability that both lights will be red when she reaches them; P(R₁,R₂) = 0.22

Probability that the first light will be red and the second light will not be red;

P(R₁R') = 0.33

     We are told that the traffic lights operate independently which means we are dealing with independent events.

Thus, formula to get the probability that the second light will be red when she reaches it is;

P(R₁) × P(R₂) = P(R₁,R₂)

Where;

P(R₂) is the probability that the second light will be red when she reaches it.

P(R₁) is the probability that the first light will be red when she reaches it = 0.33 + 0.22 = 0.55

Thus, plugging in the relevant values gives;

0.55 × P(R₂) = 0.22

P(R₂) = 0.22/0.55

P(R₂) = 0.4

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