Two dice are thrown and the sum of the number | vedclass

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(D) The sample space $S$ contains $36$ outcomes: $S = \{(x, y) : x, y \in \{1, 2, 3, 4, 5, 6\}\}$.$A = \{(1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,

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$C$ and $D$

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(D) The sample space $S$ contains $36$ outcomes: $S = \{(x, y) : x, y \in \{1, 2, 3, 4, 5, 6\}\}$.$A = \{(1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5), (4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6)\}$$B = \{(1,2), (2,1), (1,5), (5,1), (3,3), (2,4), (4,2), (3,6), (6,3), (4,5), (5,4), (6,6)\}$$C = \{(1,1), (1,2), (2,1)\}$$D = \{(6,6)\}$Two events are mutually exclusive if their intersection is the empty set $(\phi)$.Checking the intersections:$A \cap B = \{(1,5), (2,4), (3,3), (4,2), (5,1), (6,6)\} 
eq \phi$$A \cap D = \{(6,6)\} 
eq \phi$$B \cap D = \{(6,6)\} 
eq \phi$$C \cap D = \phi$Since $C \cap D = \phi$,the events $C$ and $D$ are mutually exclusive.

List-$I$	List-$II$
$(i) \ P(A \cap B)$	$(1) \ 0.4$
$(ii) \ P(A \cap \bar{B})$	$(2) \ 0.2$
$(iii) \ P(\bar{A} \cap B)$	$(3) \ 0.3$
$(iv) \ P(\bar{A} \cap \bar{B})$	$(4) \ 0.1$

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