(b) Claude goes to school by bus.
The probability that the bus is late is 0.1. If the bus is late, the
probability that Claude is late to school is 0.8.
If the bus is not late, the probability that Claude is late to school is 0.05.
i) Calculate the probability that the bus is late and Claude is late to school.
ii) Calculate the probability that Claude is late to school.
iii) The school term lasts 56 days.
How many days would Claude expect to be late?

i) 0.08 = 8% probability that the bus is late and Claude is late to school.

ii) 0.125 = 12.5% probability that Claude is late to school.

iii) Claude should expect to be late for 7 days.

Step-by-step explanation:

i) Calculate the probability that the bus is late and Claude is late to school.

0.1 probability that the bus is late.

If the bus is late, 0.8 probability that Claude is late to school. So

0.08 = 8% probability that the bus is late and Claude is late to school.

ii) Calculate the probability that Claude is late to school.

8%(when the bus is late) plus 0.05 of 1 - 0.01 = 0.9. So

0.125 = 12.5% probability that Claude is late to school.

iii) The school term lasts 56 days. How many days would Claude expect to be late?

12.5% of 56. So

0.125*56 = 7

Claude should expect to be late for 7 days.