EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Probability>JEE Advanced Paper 1 - 2021>Q 14

HARD

JEE Advanced

IMPORTANT

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Let $E, F$ and $G$ be three events having probabilities $P (E) = \frac{1}{8}, P (F) = \frac{1}{6}$ and $P (G) = \frac{1}{4},$ and let $P (E \cap F \cap G) = \frac{1}{10}$

For any event $H$ , if $H^{c}$ denotes its complement, then which of the following statements is (are) TRUE ?

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Important Questions on Probability

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Probability>JEE Advanced Paper 1 - 2020>Q 15

Let

C_{1}

and

C_{2}

be two biased coins such that the probabilities of getting head in a single toss are

\frac{2}{3}

and

\frac{1}{3}

, respectively. Suppose

α

is the number of heads that appear when

C_{1}

is tossed twice, independently, and suppose

β

is the number of heads that appear when

C_{2}

is tossed twice, independently. Then the probability that the roots of the quadratic polynomial

x^{2} - α x + β

are real and equal, is

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Probability>JEE Advanced Paper 1 - 2017>Q 18

Let

X

and

Y

be two events such that

P (X) = \frac{1}{3}

,

P (X| Y) = \frac{1}{2}

and

P (Y | X) = \frac{2}{5} .

Then