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Prove that P(A uu B) = P(A) + P(B) - P(A...

Prove that `P(A uu B) = P(A) + P(B) - P(A nn B)`

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For any two events A and B, show that, P(A uu B) = P(A) + P(B) - P(A nn B) .

For any three events A, B and C, prove that. P(A cup B cup C) = P(A) + P(B) + P( C)-P(Acap B) -P(BcapC) - P(CcapA) + P(Acap B cap C).

For any two sets A and B, prove that P(A cap B) = P(A) capP(B) where P(A) is the power set of A.

If A and B are arbitrary events, then a) P(A nn B) ge P(A)+ P(B) (b) P(A nn B) le P(A)+ P(B) (c) P(AnnB)=P(A)+ P(B) (d)None of these

If A and B are two events, then which of the following dies not represent the probability of at most one of A ,B occurs. (a) P(A) + P(B) - P(A nn B) (b) P(A nn B') + P(A' nn B) (c) P(A') + P(B') - 2P(A' nn B') (d) P(A) + P(B) -2 P(A nn B)

For any two events A and B prove that, P(A//B) lt P(B//A) " if " P(A) lt P(B)

For any two events A and b prove that, P(A) ge P(A cap B) ge P(A) + P(B) - 1

For any two events A and b prove that, P(A cap B ) le P(A) le P(A cup B ) le P(A) + P(B)

Show that for two non-mutually exclusive events A and B, P(A cup B)=P(A) +P(B)-P(A cap B)

UNITED BOOK HOUSE-Hare School, Question Paper -Exercise
  1. If P(A) = 1/2, P(B) = 2/3 then prove that 1/6 le P(A nn B) le 1/2

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  2. If 9 biscuits of different types be distributed among 3 children, find...

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  3. Show that overset(n)underset(i=1)sum (xi - A)^2 is minimum when A = ba...

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  4. If y = (x-a)/b, then prove that Sy = frac(Sx)(|b|)

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  5. Prove that P(A uu B) = P(A) + P(B) - P(A nn B)

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  6. The variance of 1, 2,…………..n is 24. Find n.

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  7. For 10 values of X, it is given that sumu = 4 and sum u^2 = 144, where...

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  8. Two groups of 15 and 22 values have variances 9 and 16 respectively. I...

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  9. For a set of an positive quantities prove that AM ge GM ge HM.

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  10. Prove that 1/n overset(n)underset(E1)sum |xi - A| attains, minimum whe...

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  11. Let x be a variable assuming the values 1, 2,……….k and let F1 = n, F2,...

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  12. |x-2| le 6 implies that

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  13. When it comes to comparing different segments among themselves and als...

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  14. Mode of a distribution can be obtained from

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  15. Frequency curve is the limiting form of

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  16. If the AM and HM of two numbers are 16 and 4 respectively, then the GM...

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  17. If the median and mode for a moderate asymmetrical distribution are 8 ...

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  18. If 2x + 3y = 6 and S.D. of X = 6, the S.D. of y is -

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  19. If the C.V. is 40 and SX^2 = 400, then barx is

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  20. If 3x - 2y + 6 = 0, R(x) = 4, then R(y) is

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