Final answer:
The probability that a teenage driver has been issued a ticket for speeding, given that they ran a red light, is calculated using the conditional probability formula and is approximately 44.44%.
Step-by-step explanation:
To calculate the probability that a teenage driver has been issued a ticket for speeding given that they have run a red light, we use the concept of conditional probability.
The formula for conditional probability is P(A|B) = P(A and B) / P(B), where P(A|B) is the probability of event A given event B has occurred, P(A and B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.
From the information provided:
- P(speeding and red light) = 4%, or 0.04
- P(red light) = 9%, or 0.09
Now we can plug these values into the formula to find the conditional probability:
P(speeding | red light) = P(speeding and red light) / P(red light)
P(speeding | red light) = 0.04 / 0.09
P(speeding | red light) = 0.4444 or 44.44%
Therefore, the probability that a teenage driver has been issued a ticket for speeding, given that they ran a red light, is approximately 44.44%.