The random variable (X) has the following probability distribution x 0 1 2 3 4 P(X=x) k 3 k 5 k 2 k k ) Then the value of (P(X ≥ 2)) is

Correct answer: B. ( (2)/(3) ) Since, P_ i ( X=x )=1) aligned & k+3 k+5 k+2 k+k=1 12 k=1 k=(1)/(12) & Now, P(X ≥2)=P(X=2)+P(X=3)+P(X=4) & =5 k+2 k+k=8 k=8((1)/(12))=(2)/(3) aligned

BITSAT 2009

Exam: BITSAT
Year: 2009
Subject: Mathematics
Chapter: Properties of Triangles

BITSAT 2009 · Mathematics · Properties of Triangles

The random variable (X) has the following probability distribution...

The random variable (\mathrm{X}) has the following probability distribution

<table class="qx-match-list qx-match-table" border="1" cellpadding="6" cellspacing="0"><tr><td>x</td><td>0</td><td>1</td><td>2</td><td>3</td><td>4</td></tr><tr><td>P(X=x)</td><td>k</td><td>3 k</td><td>5 k</td><td>2 k</td><td>k</td></tr></table>

) Then the value of (P(X \geq 2)) is

Options

A( $\frac{1}{3}$ )
B( $\frac{2}{3}$ )
C( $\frac{3}{4}$ )
D( $\frac{1}{4}$ )

Correct answer

B. ( $\frac{2}{3}$ )

Step-by-step solution

Since,

\Sigma \mathrm{P}_{\mathrm{i}}(

\mathrm{X}=\mathrm{x}

)=1)

\begin{aligned}& \therefore \mathrm{k}+3 \mathrm{k}+5 \mathrm{k}+2 \mathrm{k}+\mathrm{k}=1 \therefore 12 \mathrm{k}=1 \therefore \mathrm{k}=\frac{1}{12}\\ & \text{ Now, } \mathrm{P}(\mathrm{X} \geq2)=\mathrm{P}(\mathrm{X}=2)+\mathrm{P}(\mathrm{X}=3)+\mathrm{P}(\mathrm{X}=4) \\ & =5 \mathrm{k}+2 \mathrm{k}+\mathrm{k}=8 \mathrm{k}=8\left(\frac{1}{12}\right)=\frac{2}{3} \end{aligned}

Practice Properties of Triangles on Quantrex Academy →

More from Properties of Triangles

If in a A B C, 2 b^2=a^2+c^2 , then ( 3B)/( B) is equal to BITSAT 2022 Let ABC be an acute-angled triangle and let D be the mid-point of BC . If AB = AD , then… BITSAT 2019 In a ABC, if A a = B b = C c , and the side a=2, then area of the triangle is BITSAT 2016 In a A B C , the lengths of the two larger sides are 10 and 9 units, respectively. If the… BITSAT 2015 In a triangle ABC, if a=2, B=60^ ^ ∘ and C=75^ ^ ∘ , then b equals BITSAT 2012 In an equilateral triangle, the in radius, circumradius and one of the ex-radii are in… BITSAT 2011 Full Properties of Triangles list Properties of Triangles JEE Maths PYQs JEE Mathematics PYQs All BITSAT PYQs