Quadratic Equations
Probability with dice (misplaced question)
nta_pyq_2023_jan
Grade 11
Question:
Two dice are thrown independently. Let A be the event that the number appeared on the 1st die is less than the number appeared on the 2nd die, B be the event that the number appeared on the 1st die is even and that on the second die is odd, and C be the event that the number appeared on the 1st die is odd and that on the 2nd is even. Then:
the number of favourable cases of the event $(A \cup B) \cap C$ is 6
A and B are mutually exclusive
The number of favourable cases of the events A, B and C are 15, 6 and 6 respectively
B and C are independent
Step-by-Step Solution
Key Concept: Count favourable outcomes for each event: $n(A)=15$, $n(B)=9$, $n(C)=9$. Compute $(A\cup B)\cap C = (A\cap C)\cup(B\cap C)$.
$n(A)=15$, $n(B)=9$, $n(C)=9$. $n((A\cup B)\cap C) = n(A\cap C) + n(B\cap C) = (3+2+1)+0 = 6$. Option (1) is correct.
Correct Answer: 1