Question

One die has three faces marked with 1; two faces marked 2, and one face marked 3; another has one face marked 1, two marked 2 and three marked 3, then

• A. the most probable throw with two dice is 4
• B. the probability of most probable throw is $\frac{1}{4}$
• C. the probability of most probable throw is 7/18
• D. none of these

Answer 1

Answer: (A), (C)

The correct options are
A the most probable throw with two dice is 4
C the probability of most probable throw is 7/18

The minimum sum that can occur is 2 and maximum that can occur is 6. The number of ways in which 2, 3, 4, 5, 6 can occur are the coefficients of $x^2,x^3,x^4,x^5,x^6$ in the expansion of $(3x+2x^2+x^3)(x+2x^2+3x^3)=3x^2+8x^3+14x^4+8x^5+3x^6$.
This shows that the sum that occurs most often is 4. Also, the number of ways in which different sums can occur is $(3+2+1)(1+2+3)=36$
$\therefore$ The probability of 4 is 14/36 $=7/18$.