Let E1= Student does not know the answer E2= Student knows the answer ‌ and ‌E=‌ student answer correctly ‌ ∴‌‌P(E1)=1−p⇒P(E2)=p ⇒‌‌P(‌
E
E2
)=1‌ and ‌P(‌
E
E1
)=‌
1
5
Note that, the probability that student did not know the answer randomly = The probability that student know the answer. ∴‌‌P(‌