Find the probability of a student being late in a month

Question

In a class, there are 25 students: 7 go to school by foot, 8 go to school by bike while the remaining 10 go to school by bus. 

In a month, 1% of the students who come to school by foot are late, 2% of the students who come to school by bike are late, and 5% of the students who come to school by bus are late to school.

Requests:

• Find the probability of a studing arriving late to school
• Considering a student who is late, calculate the probability of them coming to school by bike

Could anybody help me? Thanks

Answer 1

By foot: 1% of 7=0.07 are late;

By bike: 2% of 8=0.16 are late;

By bus: 5% of 10=0.50 are late.

So, in any given period, 0.73 students are late. For example, in 100 days (2500 "trials" in about 5 school months) 73 students are late. So the probability of lateness is 73/2500=0.0292, or 2.92%.

Continuing with the example, of the 73 students who came late, 16 came by bike, so 16/73=0.22 or 22% (approx) is the probability.