Two dice are thrown independently.

Question

Two dice are thrown independently. Let $A$ be the event that the number on the 1st die is less than the number on the 2nd die, $B$ be the event that the number on the 1st die is even and the second is odd, and $C$ be the event that the number on the 1st die is odd and the second is even. Then:

Accepted Answer

$$n(A)=5+4+3+2+1=15, \qquad n(B)=3\times3=9, \qquad n(C)=3\times3=9.$$

$$(A\cup B)\cap C = (A\cap C)\cup(B\cap C).$$

$A\cap C$ (first odd, second even, first<second): pairs $(1,2),(1,4),(1,6),(3,4),(3,6),(5,6)$ --- 6 pairs.

$B\cap C=\varnothing$ (B needs first even, C needs first odd --- contradictory).

$$n\big((A\cup B)\cap C\big)=6+0=6.$$

*(This item, extracted from the source PDF under this topic's Question 83 marker, is a probability question rather than a complex-numbers/quadratic-equations question --- likely a page-boundary artifact in the original scan. It is reproduced faithfully as it appeared in the source.)*

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