JEE MATHEMATICS MCQ: PROBABILITY

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Analyzing +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

\frac{1}{2}, \frac{1}{4}

and

\frac{1}{4}

. For the ship to be operational at least two of its engines must function. Let

X

denote the event that 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 not true?

View answer and explanation

Correct option: C

P\left(X / X_2\right)=\frac{5}{16}

Option C (

P(X / X_2)=\frac{{5}}{{16}}

) is not true because the correct conditional probability

P(X/X_2)

\frac{{5}}{{8}}

, not

\frac{{5}}{{16}}

More Questions from PROBABILITY

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\begin{array}{cccccc}X: & 1 & 2 & 3 & 4 & 5 \\ P(X): & k^2 & 2 k & k & 2 k & 5 k^2\end{array}

P(X>2)

\left( {2\;n + 1} \right)

n

n + 1

n

A

B

P\left( {A \cap B'} \right) = \frac{3}{{25}}

P\left( {A' \cap B} \right) = \frac{8}{{25}}

P\left( A \right)

A

B

A

B

B

A