Question

Джон едет на работу на машине с вероятностью 0.5 и на автобусе с вероятностью 0.8. Он опаздывает в 30% случаев, когда едет на машине, но только в 10%, когда едет в автобусе. Какова вероятность того что он опаздывает на работе?

Answer 1

Ответ:

Объяснение:

4*8=32 чел в автобусе

4+32=36 чел всего

Answer 2

Problem Analysis

We are given that John has a 50% chance of going to work by car and an 80% chance of going by bus. We are also given that he is late 30% of the time when he goes by car and only 10% of the time when he goes by bus. We need to find the probability that he is late for work.

Solution

To find the probability that John is late for work, we can use the law of total probability. We will calculate the probability of being late for work when John goes by car and when he goes by bus, and then combine these probabilities using the probabilities of choosing each mode of transportation.

Let's calculate the probability of being late for work when John goes by car. We know that the probability of going by car is 0.5 and the probability of being late when going by car is 0.3. Therefore, the probability of being late for work when going by car is 0.5 * 0.3 = 0.15.

Now let's calculate the probability of being late for work when John goes by bus. We know that the probability of going by bus is 0.8 and the probability of being late when going by bus is 0.1. Therefore, the probability of being late for work when going by bus is 0.8 * 0.1 = 0.08.

To find the overall probability of being late for work, we need to combine the probabilities of being late when going by car and when going by bus, weighted by the probabilities of choosing each mode of transportation. The probability of going by car is 0.5 and the probability of going by bus is 0.8. Therefore, the overall probability of being late for work is 0.5 * 0.15 + 0.8 * 0.08 = 0.075 + 0.064 = 0.139.

Therefore, the probability that John is late for work is 0.139.

Conclusion

The probability that John is late for work is 0.139.