EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 25 July 2022 Shift 1>Q 103

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IMPORTANT

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If the sum and the product of mean and variance of a binomial distribution are $24$ and $128$ respectively, then the probability of one or two successes is :

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Important Questions on Probability

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 25 July 2022 Shift 1>Q 104

If the numbers appeared on the two throws of a fair six faced die are

α

and

β

, then the probability that

x^{2} + α x + β > 0

, for all

x \in R

, is

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JEE Main

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 25 July 2022 Shift 2>Q 105

If

A

and

B

are two events such that

P (A) = \frac{1}{3}, P (B) = \frac{1}{5}

and

P (A \cup B) = \frac{1}{2}

, then

P (A B^{'}) + P (B A^{'})

is equal to

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 26 July 2022 Shift 1>Q 106

The mean and variance of a binomial distribution are

α

and

\frac{α}{3}

respectively. If

P (X = 1) = \frac{4}{243}

, then

P (X = 4 or 5)

is equal to:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 26 July 2022 Shift 1>Q 107

Let

E_{1}, E_{2}, E_{3}

be three mutually exclusive events such that

P (E_{1}) = \frac{2 + 3 p}{6}, P (E_{2}) = \frac{2 - p}{8}

and

P (E_{3}) = \frac{1 - p}{2}

. If the maximum and minimum values of

p

are

p_{1}

and

p_{2}

then

(p_{1} + p_{2})

is equal to:

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JEE Main

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 26 July 2022 Shift 2>Q 108

Let

X

be a binomially distributed random variable with mean

4

and variance

\frac{4}{3}

. Then

54 P (X \leq 2)

is equal to

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JEE Main

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 27 July 2022 Shift 1>Q 109

Let

S

be the sample space of all five digit numbers. If

p

is the probability that a randomly selected number from

S

, is a multiple of

7

but not divisible by

5

, then

9 p

is equal to

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JEE Main

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 27 July 2022 Shift 2>Q 110

Let

X

have a binomial distribution

B (n, p)

such that the sum and the product of the mean and variance of

X

are

24

and

128

respectively. If

P (X > n - 3) = \frac{k}{2^{n}}

, then

k

is equal to

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 27 July 2022 Shift 2>Q 111

A six faced die is biased such that

3 \times P

(a prime number)

= 6 \times P

(a composite number)

= 2 \times P (1)

. Let

X

be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of

X

is