WAEC 2009 · Paper 2 · Q5

(a)
The probabilities of Rotey obtaining the highest mark in Mathematics, Physics and Biology tests are $0.9$ , $0.75$ and $0.8$ respectively. Calculate the probability of getting the highest marks in at least two subjects.

Worked solution (try it first)

The probabilities of not getting the highest mark are $1 - 0.9 = 0.1$ , $1 - 0.75 = 0.25$ and $1 - 0.8 = 0.2$ .
At least two means exactly two or all three.
The tests are independent, so multiply along each case.
Maths and Physics only: $0.9 \times 0.75 \times 0.2 = 0.135$ .
Maths and Biology only: $0.9 \times 0.25 \times 0.8 = 0.18$ .
Physics and Biology only: $0.1 \times 0.75 \times 0.8 = 0.06$ .
All three: $0.9 \times 0.75 \times 0.8 = 0.54$ .
Add the four cases: $0.135 + 0.18 + 0.06 + 0.54 = 0.915$ .