Q. One die has two faces marked 1, two faces marked 2, one face marked 3 and one face marked 4. Another die has one face marked 1, two faces marked 2, two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5, when both the dice are thrown together, is
A) $\frac23$
B) $\frac12$
C) $\frac49$
D) $\frac35$
Explanation
[Solution by Dr. Abubacker] Die 1 faces: 1,1,2,2,3,4; die 2 faces: 1,2,2,3,3,4 (36 equally likely outcomes). Sum $4$: (1,3)$\to2\cdot2=4$, (2,2)$\to2\cdot2=4$, (3,1)$\to1$: total 9. Sum $5$: (1,4)$\to2$, (2,3)$\to4$, (3,2)$\to2$, (4,1)$\to1$: total 9. Probability $=\frac{18}{36}=\frac12$. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.