It is possible for a student to either:

So we conclude that these are not mutually exclusive events. We have:

P(E1 or E2) = P(E1) + P(E2) − P(E1 and E2)

Substituting:

`4/5=2/3+4/9-P(E_1 "and" E_2)`

So

`P(E_1 "and" E_2)` ` = 2/3 + 4/9-4/5` `=14/45`