Question

There are two die $A$ and $B$ both having six faces. Die $A$ has three faces marked with $1$, two faces marked with $2$, and one face marked with $3$. Die $B$ has one face marked with $1$, two faces marked with $2$, and three faces marked with $3$. Both dices are thrown randomly once. If $E$ be the event of getting sum of the numbers appearing on top faces equal to $x$, let $P\left(E\right)$ be the probability of event $E$, then
$P\left(E\right)$ is maximum when $x$ equal to

• A. $5$
• B. $3$
• C. $4$
• D. $6$

Answer 1

The correct option is C $4$

$x$ can be $2,3,4,5,6.$ The number of ways in which sum of $2,3,4,5,6$ can occur by the coefficients of $x^2,x^3,x^4,x^4,x^5,x^6$ in
$(3x+2x^2+x^3)(x+2x^2+3x^3)=3x^2+8x^3+14x^4+8x^5+3x^6$
This shows that the sum that occurs most often is $4$