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# Two dice are thrown together and the total score is noted.The events E,F and G are 'a total of 4','a total of 9 or more',and 'a total divisible by 5'respectively.Calculate P(E),P(F) and P(G) and decide which pairs of events,if any, are independent.

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• In a pair of die thrown together total number of events 6x6=36
• E=getting a total of 4
• E=${(1,3),(3,1),(2,2)}$
• F=Total of 9or more
• ${(3,6),(6,3),(4,5),(5,4),(5,5)(6,4),(4,6),(5,6)(6,5),(6,6)}$
• G=Total disable by 5
• Total of 5or10
• ${(1,4),(4,1),(2,3),(3,2),(5,5),(6,4),(4,6)}$
• E$\cap$F=0
• F$\cap$G=${(5,5),(6,4),(4,6)}$
• E$\cap$G=0
• EventA and B are indenpent if P(A)P(B)=P(A$\cap$B)
P(E)=$\Large\frac{3}{36}$=$\Large\frac{1}{12}$
P(F)=$\Large\frac{10}{36}$
P(G)=$\Large\frac{7}{36}$
P(E$\cap$F)=0e
P(E$\cap$G)=0
P(F$\cap$G)=$\Large\frac{3}{36}$=$\Large\frac{1}{12}$
P(E)P(F)=$\Large\frac{10}{36}\times$$\Large\frac{1}{12}$
=$\Large\frac{5}{216}$$\neq$ P(E$\cap$F)
P(E)P(G)=$\Large\frac{1}{12}$x$\Large\frac{7}{36}$$\neq$p(E$\cap$G)
EandG arenot independent
P(F)P(G)=$\Large\frac{10}{36}$x$\Large\frac{7}{36}$$\neq$P(F$\cap$G)
F and G are not independent

edited Jun 5, 2013