Marley drives to work every day and passes two independently operated traffic lights. The probability that both lights are red is 0.35. The probability that the first light is red is 0.48. What is the probability that the second light is red, given that the first light is red?
.48x = .35
x = .35/.48 = appr .73
To find the probability that the second light is red, given that the first light is red, we can use conditional probability. Conditional probability is defined as the probability of an event A happening given that event B has already occurred, and it is denoted as P(A|B).
In this case, we want to find the probability that the second light is red (event A), given that the first light is red (event B). We can express this as P(A|B).
The formula for conditional probability is:
P(A|B) = P(A∩B) / P(B)
Where P(A∩B) represents the probability that both events A and B occur together, and P(B) represents the probability of event B occurring.
We are given that the probability that both lights are red is 0.35 (P(A∩B) = 0.35) and the probability that the first light is red is 0.48 (P(B) = 0.48).
Now we can substitute these values into the formula:
P(A|B) = P(A∩B) / P(B)
= 0.35 / 0.48
Therefore, the probability that the second light is red, given that the first light is red, is 0.35 / 0.48 ≈ 0.729.
So, the answer is approximately 0.729.
To find the probability that the second light is red, given that the first light is red, we can use conditional probability.
Let A be the event that the first light is red, and B be the event that the second light is red.
We are given that P(A) = 0.48 and P(A ∩ B) = 0.35.
The conditional probability of B given A, denoted as P(B|A), is defined as:
P(B|A) = P(A ∩ B) / P(A)
Substituting the given values:
P(B|A) = 0.35 / 0.48 = 0.729
Therefore, the probability that the second light is red, given that the first light is red, is 0.729 or approximately 72.9%.