Video Transcript
Jennifer travels to school by car or on foot. The probability that she travels by car is 0.4, and the probability that she walks is 0.6. If she travels by car, the probability that she is late is 0.2. If she travels on foot, the probability that she is late is 0.3. Using a tree diagram, calculate the probability that she is late given that she traveled by car.
There are many ways to answer this question. However, as we are asked to draw a tree diagram, we will begin by doing this. We know that Jennifer travels to school either by car or on foot. The probability that she travels by car is 0.4, and the probability she walks is 0.6. Next, we are told the probability that Jennifer is late depending on how she travels to school. As these values are different, we know that the two events are dependent. Whether Jennifer is late does depend on how she travels to school.
When she travels by car, the probability that she is late is 0.2. And when she walks to school, the probability she is late is 0.3. We know that on a tree diagram, the sum of the probabilities for each set of branches must equal one. This means that if Jennifer travels by car, the probability that she is not late is 0.8. And if Jennifer walks to school, the probability she is not late is 0.7. We are asked to find the probability that Jennifer is late given that she travels by car.
This is an example of conditional probability. Using the tree diagram, we begin by following the branch for traveling by car. And our answer will be the branch that follows this for being late. The probability that Jennifer is late given that she traveled by car is 0.2. Whilst it is not required for this question, we recall our formula for the conditional probability of dependent events states that the probability of 𝐴 given 𝐵 is equal to the probability of 𝐴 intersection 𝐵 divided by the probability of 𝐵.
