Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

BITSAT 2010

Exam: BITSAT
Year: 2010
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

BITSAT 2010 · Mathematics · Trigonometric Ratios & Identities

If ( P(A B)=(2)/(3), P(A B)=(1)/(6) ) and ( P(A)=(1)/(3) ) then

If (

\mathrm{P}(\mathrm{A} \cup \mathrm{B})=\frac{2}{3}, \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{6}

) and (

\mathrm{P}(\mathrm{A})=\frac{1}{3}

) then

Options

AA and ( $\mathrm{B}$ ) are independent events
BA and ( $\mathrm{B}$ ) are disjoint events
CA and ( $\mathrm{B}$ ) are dependent events
DNone of these

Correct answer

A. A and ( $\mathrm{B}$ ) are independent events

Step-by-step solution

(

\mathrm{P}(\mathrm{A} \cup \mathrm{B})=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{AB})

) (\Rightarrow

\frac{2}{3}=\frac{1}{3}+\mathrm{P}(\mathrm{B})-\frac{1}{6} \Rightarrow \mathrm{P}(\mathrm{B})=\frac{1}{2}

) Now, (

\mathrm{P}(\mathrm{AB})=\mathrm{P}(\mathrm{A})

~

\mathrm{P}(\mathrm{B}), \mathrm{A}

) and (

\mathrm{B}

) are independent events.

Practice Trigonometric Ratios & Identities on Quantrex Academy →

More from Trigonometric Ratios & Identities

Let A, B and C are the angles of a triangle and (A)/(2)=(1)/(3), (B)/(2)=(2)/(3) . Then… BITSAT 2024 The sum of all values of x in [0,2 π] , for which x+ 2 x+ 3 x+ 4 x=0 , is equal to : BITSAT 2024 If A+B+C=(π)/(2) then BITSAT 2021 The equation ^ 4 x-(k+2) ^ 2 x-(k+3)=0 possesses a solution if BITSAT 2020 Let (α + β) = (4)/(5) and let (α - β) = (5)/(13) , where 0 ≤ α, β ≤ (π)/(4) , then 2α = BITSAT 2019 If A and B are positive acute angles satisfying 3 ^ 2 A+2 ^ 2 B=4 and (3 A)/( B)=(2 B)/(… BITSAT 2016 If ( A)/( B)=n, ( A)/( B)=m , then the value of (m^ 2 -n^ 2 ) ^ 2 B is BITSAT 2015 ^ 2 ((π)/(6)+θ)- ^ 2 ((π)/(6)-θ)= BITSAT 2014 An arch of a bridge is semi-elliptical with major axis horizontal. If the length the base… BITSAT 2014 If x ^ 3 θ+y ^ 3 θ= θ θ and x θ=y θ, then x^ 2 +y^ 2 = BITSAT 2013 An object is obseved from the points A, B and C lying in a horizontal straight line which… BITSAT 2013 If ^ 2 θ+ ^ 2 φ=1 / 2, ^ 2 θ+ ^ 2 φ=3 / 2, then ^ 2 (θ-φ) is equal to BITSAT 2012 If, A=(1)/(2) and B= (1)/(3) , then find the value of A+B BITSAT 2011 ( θ)/(1- θ)+( θ)/(1- θ) is equal to BITSAT 2011 If the function f:(-∞, ∞) arrow B defined by f(x)=-x²+6 x-8 is bijective, then B= BITSAT 2009 Full Trigonometric Ratios & Identities list Trigonometric Ratios & Identities JEE Maths PYQs JEE Mathematics PYQs All BITSAT PYQs