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Home  >>  CBSE XII  >>  Math  >>  Probability
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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

 

answered Feb 24, 2013 by poojasapani_1
edited Jun 5, 2013 by poojasapani_1
 

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