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Questions  >>  CBSE XII  >>  Math  >>  Probability
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Q)

For a loaded die,the probabilities of outcomes are given as under P(1)=P(2)=0.2,P(3)=P(5)=P(6)=0.1 and P(4)=0.3.The die is thrown two times.Let A and B be the events,'same number each time',and 'a total score is 10 or more',respectively.If the die were fair,determine whether or not the events A and B are independent.

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A)
Toolbox:
  • If\(\ P(A)-P(B)=P(A\cap\)B)
  • Then and B are independent
  • Die thrown 2 times
  • sample space has 36 events
  • S=\({(1,1)(2,2),\dots(6,6)}\)
  • A=same number in each throw
  • =\({(1,1)(2,2),\dots(6,6)}\)
  • B=total of 10 more
  • =\({(5,5),(4,6),(6,4),(6,5),(5,6),(6,6)}\)
  • \(A\cap\)B=\({(5,5),(6,6)}\)
P(A)=\(p(1,1)+p(2,2)\dots+p(6,6)\)
=\(\frac{1}{6}\)x\(\frac{1}{6}\)+\(\frac{1}{6}\)x\(\frac{1}{6}\)..+\(\frac{1}{6}\)x\(\frac{1}{6}\)
=\(\frac{6}{36}\)
=\(\frac{1}{6}\)
P(B)=\(\frac{6}{36}\)
=\(\frac{1}{6}\)
P(A\(\cap\)B)=\(\frac{2}{36}\)
=\(\frac{1}{12}\)
P(A)P(B)=\(\frac{1}{6}\)x\(\frac{1}{6}\)
=\(\frac{1}{36}\)
\(P(A)P(B)\neq P(A\cap\)B)
AandB are not independent
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