A black and a red die are rolled simultaneously. The probability of obtaining a sum greater than 9, given that the black resulted in a 5 is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 1/3
Let F be the event “the black die shows 5” and E the event “the sum is greater than 9”. Writing outcomes as (black, red), F has 6 outcomes out of 36:
\(F = \{(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)\}\)
Of these, the sum is greater than 9 only when the red die shows 5 or 6:
\(E \cap F = \{(5,5), (5,6)\}\)
By the definition of conditional probability:
\(\displaystyle P(E|F) = \frac{P(E \cap F)}{P(F)} = \frac{2/36}{6/36}\)
\(\displaystyle = \frac{2}{6} = \frac{1}{3}\)
NCERT (2026-27 edition):
Conditional Probability
