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A ship is fitted with three engines `E_1`, `E_2`, and `E_3`,. The engines function independently of each other with respective probabilities `1/2`. `1/4`and `1/4` ,and For the ship to be operational at least two of its engines must function. Let X denote the event that the ship is operational and let `X_1`, `X_2`, and `X_3` denote respectively the events that the engines `E_1`, `E_2` and `E_3`,are functioning. Which of the following is (are) true?

A

`P[X_(1)^(c )//X]=(3)e/(16)`

B

`P["exactly two engines of the ship are functioning"//X]=(7)/(8)`

C

`P[X //X_2]=(5)/(16)`

D

`P[X //X_1]=(7)/(16)`

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The correct Answer is:
B, D
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ARIHANT MATHS-PROBABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. Let A, B, C be pariwise independent events with P(C) >0 and P(AnnBnnC)...

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  3. A ship is fitted with three engines E1, E2, and E3,. The engines funct...

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  4. four fair dice D1, D2,D3 and D4 each having six faces numbered 1,2,3,4...

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  5. If X and Y are two events such that PX//Y)=(1)/(2), P(Y//X)=(1)/(3) an...

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  6. Three numbers are chosen at random without replacement from {1, 2, 3, ...

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  8. Four person independently solve a certain problem correctly with pr...

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  9. Of the three independent events E1, E2 and E3, the probability that on...

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  10. A box B(1) contains 1 white ball, 3 red balls, and 2 black balls. An- ...

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  11. A box B1 contains 1 white ball, 3 red balls and 2 black balls. Another...

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  12. Let A and B be two events such that Poverline((AcupB))=(1)/(6),P(AcapB...

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  13. Three boys and two girls stand in a queue. The probability, that the n...

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  15. Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains fiv...

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  16. If 12 identical balls are to be placed in 3 identical boxes, then t...

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  17. The minimum number of times a fair coin needs to be tossed, so that th...

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  18. Let n1, and n2, be the number of red and black balls, respectively, i...

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  19. Let n1, and n2, be the number of red and black balls, respectively, i...

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  20. Let two fair six-faced dice A and B be thrown simultaneously. If E1 is...

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