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Prove that, if P(A//B)=P(A) then P(A^c/...

Prove that, if `P(A//B)=P(A)` then `P(A^c//B)=P(A^c)`.

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UNITED BOOK HOUSE-SET 16-EXERCISE
  1. If the vectors 3 hati - 2hatj + mhatk and -2 hati + hatj + 4 hatk are ...

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  2. Can the numbers 1/2,-1/sqrt2, -1/2 be the direction cosines of a strai...

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  3. Prove that, if P(A//B)=P(A) then P(A^c//B)=P(A^c).

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  4. If the probability of success in a single trials is 0.05, how many Ber...

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  5. Prove that, |[sin A, cosA, sin(A+theta)],[sinB, cosB, sin(B+theta)],[s...

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  6. If A,B,C be the angles of a triangle, then prove that ,abs((-1,cosC,co...

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  7. Solve:|[a+x,a-x,a-x],[a-x,a+x,a-x],[a-x,a-x,a+x]|=0

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  8. If A = |[1,2,-3],[2,3,2],[3,-3,-4]|, find A^(-1)

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  9. If f(x) = xsqrt (x^2+a^2) +a^2 log(xsqrt(x^2+a^2))then find the value ...

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  10. If y = a cos(logx) + b sin(log x), show that,x^2(d^2y)/(dx^2)+x(dy)/(d...

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  11. Integrate:int(2x^2 - 3x+9)/(x^2+4x-5)dx

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  12. Evaluate: int[(x-l)(x-m)]/[(x-a)(x-b)]dx

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  13. Solve:(1+x^2)(dy)/(dx) + 2xy = sqrt (x^2+4)

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  14. Solve: log(dy)/(dx) = 4x - 2y-2: given y = 1, when x = 1.

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  15. (d) answer any one question : (i) if three vectors vec a, vec b and ve...

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  16. The position vectors of the points A,B,C and D are 6 hati - 7 hatj, 16...

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  17. Show that, int0^(pi/2)(sin 2x dx)/(sin^4x + cos^4 x) = pi/2

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  18. Evaluate: overset(pi/4)underset(0)intlog(1+tan theta)d theta.

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  19. The probability that three is at least one error in an accounts statem...

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  20. A normal to the parabola y^2 = 5x makes an angle 45^@ with line x-axis...

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