New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Probability question

2012 · Shift 2 · Q25

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Advanced
Mathematics
Probability
2012 · Shift 2 · Q25

Probability question

2012 · Shift 2 · Q25

JEE AdvancedMathematicsProbabilityMultiple correct+4 / −1

Let

X

and

Y

be two events such that

P\left( {X|Y} \right) = {1 \over 2},P\left( {Y|X} \right) = {1 \over 3}

and

P\left( {X \cap Y} \right) = {1 \over 6}.

Which of the following is (are) correct ?

A
$P\left( {X \cup Y} \right) = {2 \over 3}$
B
$X$ and $Y$ are independent
C
$X$ and $Y$ are not independent
D
$P\left( {{X^c} \cap Y} \right) = {1 \over 3}$

More from Probability

Four fair dice $D_{1}, D_{2}, D_{3}$ and $D_{4}$ ; each having six faces numbered $1, 2, 3, 4, 5$ and $6$ are rolled simultaneously. The probability that $D_{4}$ shows a number appearing on one of $D_{1}, D_{2}$ and $D_{3}$ is2012 · MCQ
Let $U_{1}$ and $U_{2}$ be two urns such that $U_{1}$ contains $3$ white and $2$ red balls, and $U_{2}$ contains only $1$ white ball. A fair coin is tossed. If head appears then $1$ ball is drawn at random from $U_{1}$ and put into…2011 · MCQ
Let $U_{1}$ and $U_{2}$ be two urns such that $U_{1}$ contains $3$ white and $2$ red balls, and $U_{2}$ contains only $1$ white ball. A fair coin is tossed. If head appears then $1$ ball is drawn at random from $U_{1}$ and put into…2011 · MCQ
Let $E$ and $F$ be two independent events. The probability that exactly one of them occurs is $\frac{11}{25}$ and the probability of none of them occurring is $\frac{2}{25}$ . If $P (T)$ denotes the probability of occurrence of…2011 · Multiple correct
Let $ω$ be a complex cube root of unity with $ω e 1.$ A fair die is thrown three times. If $r_{1}, r_{2}$ and $r_{3}$ are the numbers obtained on the die, then the probability that $ω^{r_{1}} + ω^{r_{2}} + ω^{r_{3}} = 0$ …2010 · MCQ
A signal which can be green or red with probability $\frac{4}{5}$ and $\frac{1}{5}$ respectively, is received by station A and then transmitted to station $B$ . The probability of each station receving the signal correctly is $\frac{3}{4}$ .…2010 · MCQ
A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.The conditional probability that $X \geq 6$ given $X > 3$ equals :2009 · MCQ
A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.The probability that $X \geq 3$ equals :2009 · MCQ