GATE | GATE MOCK 2017 | Question 20

mock_2

(A) A
(B) B
(C) C
(D) D


Answer: (A)

Explanation:
The \ sample \ space \ is \ given \ by \\ S=\left \{ (x,y):1<=x<=6 \ and \ 1<=y<=6 \right \} \ and \ n(s)=36 \\ A=\left \{ (1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(3,6), \\ (4,1),(4,3),(4,5),(5,2),(5,4),(5,6),(6,1),(6,3),(6,5) \right \} \\ B=\left \{ (1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(3,1),(4,1),(5,1),(6,1),(1,1) \right \} \\ A\cap B=\left \{ (1,2),(1,4),(1,6),(2,1),(4,1),(6,1) \right \} \\ P(A)=\frac{n(A)}{n(S)}=\frac{18}{36}=\frac{1}{2},P(B)=\frac{n(B)}{n(S)}=\frac{11}{36},P(A\cap B)=\frac{n(A\cap B)}{n(S)}=\frac{6}{36}=\frac{1}{6} \\ P(A\cap \bar{B})=P(A)-P(A\cap B)=\frac{1}{2}-\frac{1}{6}=\frac{1}{3} \\ P(\bar{A} \cap \bar{B})=P(\overline{A\cup B})=1-P(A\cap B)=1-\frac{23}{36}=\frac{13}{36} \\ P(B/A)=\frac{P(A\cap B)}{P(A)}=\frac{1/6}{1/2}=\frac{1}{3}


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