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 and let $$P(E)$$ be the probability of event E, $$thenP(E)$$ is maximum when x equal $$toP(E)$$ is minimum when x equals toWhen x $$=$$ $$4$$, then $$P(E)$$ is equal to

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Infinity Learn · Accepted Answer

x can be $$2$$, $$3$$ , $$4$$, $$5$$ , $$6$$. The number of ways in which sum of $$2$$, $$3$$, $$4$$, $$5$$, $$6$$ can occur is given by the coefficients of $$x2$$, $$x3$$, $$x4$$, $$x5$$, $$x6$$ in $$3x+2x2+x3x+2x2+3x3=3x2+8x3+14x4+8x5+3x6This$$ shows that sum that occurs most often is $$4$$.Sum that occurs for minimum times is $$2$$ or $$6$$.The number of ways in which different sums can occur is (3$$ $$+$$ $$2$$ $$+$$ $$1) (1$$ $$+$$ $$2$$ $$+$$ $$3) $$=$$ $$36$$. The probability of $$4$$ $$is14/36$$ $$=$$ $$7/18$$.

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