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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