Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 9 - Probability I>Exercises>Q 22

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

If the papers of $4$ students can be checked by any one of the $7$ teachers, then the probability that all the $4$ papers are checked by exactly $2$ teachers is

50% studentsanswered this correctly

Important Questions on Probability I

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 9 - Probability I>Exercises>Q 23

If the events

A

and

B

are mutually exclusive events such that

P (A) = \frac{3 x + 1}{3}

and

P (B) = \frac{1 - x}{4},

then the set of possible real values of

x

lies in the interval

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 9 - Probability I>Exercises>Q 24

A natural number

x

is chosen at random from the first

100

natural numbers. The probability that

x + \frac{100}{x} > 50

is

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 9 - Probability I>Exercises>Q 25

A dice is thrown six times, it being known that each time different digit is shown. The probability that a sum of

12

will be obtained in the first three throws is

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 9 - Probability I>Exercises>Q 26

If

a \in I

and

a \in [- 5, 30]

, then the probability that the graph of

y = x^{2} + 2 (a + 4) x - 5 a + 64

is strictly above the

x

-axis is

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 9 - Probability I>Exercises>Q 27

Four die are thrown simultaneously. The probability that

4

and

3

appear on two of the die given that

5

and

6

have appeared on other two die is

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 9 - Probability I>Exercises>Q 28

A

2 n

digit number starts with

2

and all its digits are prime, then the probability that the sum of all

2

consecutive digits of the number is prime is

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 9 - Probability I>Exercises>Q 29

In a

n

-sided regular polygon, the probability that the two diagonal chosen at random will intersect inside the polygon is

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 9 - Probability I>Exercises>Q 30

A three-digit number is selected at random from the set of all three-digit numbers. The probability that the number selected has all the three digits same is