Let 0 < P ( A ) < 1 , 0 < P ( B ) < 1 & P ( A ∪ B ) = P ( A ) + P ( B ) - P ( A ) · P ( B ) , then

P ( B / A ) = P ( B ) - P ( A )

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.

HARD

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IMPORTANT

Earn 100

A Teacher wrote either of words "PARALLELOGRAM" or "PARALLELOPIPED" on board but due to malfunction of marker words is not properly written and only two consecutive letters "RA" are visible then the chance that the written word is "PARALLELOGRAM" is $\frac{p}{q}$ then $(p + q)$ equals. (Where $p & q$ are co-prime natural numbers)-

32.69% studentsanswered this correctly

Important Questions on Probability

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-2>Q 31

The numbers

' a

and

b

' are randomly selected from the set of natural numbers. Probability that the number

3^{a} + 7^{b}

has a digit equal to

8

at the units place, is

\frac{p}{q}

then

p + q

is (Where

p & q

are co-prime natural numbers)-

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-2>Q 33

A bag contains undefined coins. It is known that one of these coins shows head on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probability that the toss results in head is

\frac{7}{12}

then find the value of

n

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-2>Q 35

In each of a set of games it is

2

1

in favor of the winner of the previous game. If the probabilty that the player who wins the first game shall win three at least of the next four is

\frac{p}{q}

then

p q

equals (Where

p & q

are co-prime natural numbers)-

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-2>Q 36

A couple has one or two or three children with probability

\frac{1}{4}, \frac{1}{2}

and

\frac{1}{4}

respectively. Probability of a couple having exactly four grandchildren in such a type of society is

\frac{p}{q}

then sum of digit of qequals. (Where

p & q

are co-prime natural numbers)

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-2>Q 37

In throwing a dice, let

A

be the event 'coming up of an odd number',

B

be the event 'coming up of an even number',

C

be the event 'coming up of a number

\geq 4^{'}

and

D

be the event 'coming up of a number

< 3

', then

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-2>Q 38

M & N

are any two events, then which one of the following represents the probability of the occurrence of exactly one of them?

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-2>Q 39

Let

0 < P (A) < 1, 0 < P (B) < 1 & P (A \cup B) = P (A) + P (B) - P (A) \cdot P (B),

then

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 10 - Probability>Exercise-2>Q 40

A box contains

11

tickets numbered from

1

11 .

Two tickets are drawn simultaneously at random. Let

E_{1}

denotes the event that the sum of the numbers on the tickets drawn is even and

E_{2}

denotes the event that the sum of the numbers on the tickets drawn is odd Which of the following hold good?

Important Questions on Probability

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