Suppose that Jamal can choose to get home from work by taxi or bus. When he chooses to get home by taxi, he arrives home after 7 p.m. 15 percent of the time. When he chooses to get home by bus, he arrives home after 7 p.m. 8 percent of the time. Because the bus is cheaper, he uses the bus 70 percent of the time.

What is the approximate probability that Jamal chose to get home from work by bus, given that he arrived home after 7 p.m.?

The approximate probability that Jamal took the bus given that he arrived home after 7 p.m. is approximately 55.4 percent. The calculation involves principles of conditional probability.

Explanation:

The subject at hand is a probability question. Jamal can either get home by bus or taxi, and both carry different probabilities of him arriving home after 7 p.m. To solve this, we would use the formula for conditional probability. According to the question, Jamal takes the bus 70 percent of the time and the probability of him being late when he takes the bus is 8 percent, so the overall probability of Jamal being late given he took the bus is 0.70 * 0.08 = 0.056, or 5.6 percent.

Similarly, the probability of Jamal being late given he took a taxi is 0.30 * 0.15 = 0.045, reflecting that he takes the taxi 30 percent of the time (since he doesn't take the bus) and he is late 15 percent of those times.

Finally, to find the probability that Jamal took the bus given that he arrived after 7 p.m., we need to divide the probability he took the bus and was late by the total probability of being late - this gives us 0.056 / (0.056 + 0.045) = 0.554, or approximately 55.4 percent, which is the answer to this problem.

Learn more about Conditional Probability here:

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