Question

The probability of a pupil being late is 8%. Calculate the probability that in a group of 10 students, the number of pupils begin late is less than two.

Answer 1

The probability of the number of pupils being late being less than two is the same as the probability of zero students being late plus the probability of one student being late.

Let p be the probability of ONE student being late. 1-p is then the probability of ONE student not being late.

The probability of zero students being late is (1-p) multiplied by itself over 10 times. So, (1-p)^10

The probablitity of 1 student being late is the probability of 9 being on time, times the probability of one being late. Which is (1-p)^9 * (p)^1

The sum of the two will then give you the result you want.

\[(1-p)^10 + (1-p)^9 p = 0.92^10 + 0.92^10 * 0.08 = 0.4344 + 0.0378 = 0.4722\]

So, 47.2%

Answer 2

Is it just me or is x^10 comming up as (x^1)0 ? lolol. I think you understand what I meant to write, though.