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# Two dice are tossed.Find whether the following two events A and B are independent.$A=(x,y):x+y=11\quad B=(x,y):x=5$where (x,y) denotes a typical sample point.

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A)
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• If two dice are tossed number of ways u can get a total of 11
• $A;(X,4);X+y=11$
• ={$(5\;6)(6\;5)$}
• Sample space of two dice toss has 6x6=36 events
• $B;(x,y);x+y=5$
• Number of ways u can get total of five
• B={$(1\;4)(4\;1)(2\;3)(3\;2)$}
• To check if A and B are indipendany check if P(A$\cap$B)=P(A).P(B)
P(A)=$\Large\frac{2}{36}$=$\Large\frac{1}{18}$
P(B)=$\Large\frac{4}{36}$=$\Large\frac{1}{9}$

(A$\cap$B) is a null set
P(A$\cap$B)=0
P(A)$\times$P(B)$\neq$P(A$\cap$B)
A and B are not independentnd