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JEE Advanced

IMPORTANT

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A box contains $24$ identical balls of which $12$ are white and remaining black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the $4^{th}$ time on the $7^{th}$ draw, is

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Important Questions on Advanced Probability

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 16 - Advanced Probability>Target Exercises>Q 24

The probability that a man will live

10

more years are

\frac{1}{4}

and the probability that his wife will be live

10

more years are

\frac{1}{3}

. Then, the probability that none of them will be alive after

10

years, is

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 16 - Advanced Probability>Target Exercises>Q 25

A fair coin is tossed. If the result is a head, a pair of fair dice is rolled and the number obtained by adding the numbers on the two faces is noted. If the result is a tail, a card from a well-shuffled pack of

11

cards numbered

2, 3, 4, \dots, 12,

is picked up and the number on the card is noted. The probability that the noted number is

7

8

, is

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 16 - Advanced Probability>Target Exercises>Q 26

A man throws a fair coin a number of times and gets

2

points for each head he throws and

1

point for each tail he throws. The probability that he gets exactly

6

points, is

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 16 - Advanced Probability>Target Exercises>Q 27

One function is selected from all the functions

F : S \to S,

where

S = \{1, 2, 3, 4, 5, 6\}

. The probability that it is onto function, is

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 16 - Advanced Probability>Target Exercises>Q 28

One hundred identical coins, each with probability

p

, of showing up a head, are tossed. If

0 < p < 1

and the probability of heads on exactly

50

coins is equal to that of heads on exactly

51

coins, then the value of

p

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 16 - Advanced Probability>Target Exercises>Q 29

Let the probability

P_{n}

that a family has exactly

n

children be

α p^{n}

, where

n \geq 1

and

P_{0} = 1 - α p (1 + p + p^{2} + \dots)

. Suppose that all the distributions of

n

children have the same probability. If

k \geq 1

, then the probability that a family contains exactly

k

boys, is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 16 - Advanced Probability>Target Exercises>Q 30

A pair of dice is rolled together till a sum of either

5

7

is obtained. The probability that

5

comes before

7

, is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 16 - Advanced Probability>Target Exercises>Q 31

The probability of the occurrence of an event

A

0.5

and that of occurrence of another event

B

, is

0.3

. If

A

and

B

are mutually exclusive events, then the probability that none of

A

and

B

will occur, is

A box contains 24 identical balls of which 12 are white and remaining black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the 4th time on the 7th draw, is

Important Questions on Advanced Probability

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A box contains $24$ identical balls of which $12$ are white and remaining black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the $4^{th}$ time on the $7^{th}$ draw, is