Two buses A and B are scheduled to arrive at a town central bus station at noon. The probability that bus B will be late is 7 25 and the probability that bus A is late is 0 . 2 and the probability that the bus B is late given that bus A is late is 9 10 . Then,

probability that at least one bus is late is 3 10

probability that at least one bus is in time is 4 5

Two buses A and B are scheduled to arrive at a town central bus station at noon. The probability that bus B will be late is 7 25 and the probability that bus A is late is 0 . 2 and the probability that the bus B is late given that bus A is late is 9 10 . Then,

probability that at least one bus is late is 3 10

Let A and B be two events such that P A ∪ B = 1 6 , P A ∩ B = 1 4 , and P A = 1 4 , where A ¯ stands for complement of event A . Then events A and B are

independent but not equally likely.

mutually exclusive and independent.

equally likely but not independent.

equally likely and mutually exclusive.

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

Two buses $A$ and $B$ are scheduled to arrive at a town central bus station at noon. The probability that bus $B$ will be late is $\frac{7}{25}$ and the probability that bus $A$ is late is $0.2$ and the probability that the bus $B$ is late given that bus $A$ is late is $\frac{9}{10}$ . Then,

50% studentsanswered this correctly

Important Questions on Probability II

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 15

A fair coin is tossed

99

times. Let

X

be the number of times heads occurs. Then

P (X = r)

is maximum when

r

is,

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 16

The probability of choosing an integer

' k'

out of

2 m

integers

\{1, 2, 3, \dots . ., 2 m\}

is inversely proportional to

k^{4} (1 \leq k \leq m)

. If

x_{1}

is the probability that chosen number is odd and

x_{2}

is the probability that chosen number is even, then

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 17

A lot contains $50$ defective and $50$ non-defective bulbs.Two bulbs are drawn at random, one at a time, with replacement.The events $A, B & C$ are defined as follows:

$A =$ (first bulbs is defective)

$B =$ (second bulb is non-defective)

$C =$ (two bulbs are both defective or both non-defective)

Then,

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 1

If two loaded dice each have the property that

2

4

is three times as likely to appear as

1, 3, 5,

6

on each roll. When two such dice are rolled, the probability of obtaining a total of

7

p

, then the value of

[\frac{1}{p}]

is, where

[x]

represents the greatest integer less than or equal to

x .

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 2

An urn contains three red balls and

n

white balls. Mr.

A

draws two balls together from the urn. The probability that they have the same colour is

\frac{1}{2}

.Mr.

B

draws one balls from the urn, notes its colour and replaces it. He then draws a second ball from the urn and finds that both balls have the same colour is

\frac{5}{8}

. The possible value of

n

is______________.

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 3

Suppose

A

and

B

are two events with

P (A) = 0.5

and

P (A \cup B) = 0.8 .

Let

P (B) = p

A

and

B

are mutually exclusive and

P (B) = q

A

and

B

are independent events, then the value of

\frac{q}{p}

is,

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 4

Thirty-two players ranked

1

32

are playing in a knockout tournament. Assume that in every match between any two players, the better ranked player wins. The probability that ranked

1

and ranked

2

players are winner and runner up respectively is

p,

then the value of

[\frac{2}{p}]

is, where

[.]

represents the greatest integer function,

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 5

A

and

B

are two events such that

P (A) = 0.6

and

P (B) = 0.8,

if the greatest value that

P (\frac{A}{B})

can have is

p,

then the value of

8 p

is,

Two buses A and B are scheduled to arrive at a town central bus station at noon. The probability that bus B will be late is 725 and the probability that bus A is late is 0.2 and the probability that the bus B is late given that bus A is late is 910. Then,

Important Questions on Probability II

Learn and Prepare for any exam you want !

Two buses $A$ and $B$ are scheduled to arrive at a town central bus station at noon. The probability that bus $B$ will be late is $\frac{7}{25}$ and the probability that bus $A$ is late is $0.2$ and the probability that the bus $B$ is late given that bus $A$ is late is $\frac{9}{10}$ . Then,