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Probability question

2012 · Shift 1 · Q24

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PYQ Library
JEE Advanced
Mathematics
Probability
2012 · Shift 1 · Q24

Probability question

2012 · Shift 1 · Q24

JEE AdvancedMathematicsProbabilityMultiple correct+4 / −1

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 \over 2},{1 \over 4}

and

{1 \over 4}

. 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
$P\left[ {X_1^c|X} \right] = {3 \over {16}}$
B
$P$ [exactly two engines of the ship are functioning $\left. {|X} \right] = {7 \over 8}$
C
$P\left[ {X|{X_2}} \right] = {5 \over {16}}$
D
$P\left[ {X|{X_1}} \right] = {7 \over {16}}$

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