JEE MATHEMATICS MCQ: PROBABILITY

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Application +4 | -1

\mathrm{x}_1, \mathrm{x}_2, \mathrm{x}_3, \ldots \ldots \mathrm{x}_{50}

are fifty real numbers such that

x_r < x_{r+1}

for

r=1,2,3, \ldots .49

. Five numbers out of these are picked up at random and they are arranged in increasing order. The probability that the five numbers have

x_{20}

as the middle number is :

View answer and explanation

Correct option: B

\frac{{ }^{30} \mathrm{C}_2 \times{ }^{19} \mathrm{C}_2}{{ }^{50} \mathrm{C}_5}

Option B (

\frac{{{{}^{19}C_2 \times {{}^{30}C_3}}}}{{{{}^{50}C_5}}}

) is correct because it correctly calculates the probability of selecting five numbers with

x_{{20}}

as the middle number.

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