If E and F are events with P E ≤ P F and P E ∩ F > 0 , then

none of the above implications holds.

occurrence of E ⇒ occurrence of F

occurrence of F ⇒ occurrence of E

non - occurrence of E ⇒ non - occurrence of F

HARD

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IMPORTANT

Earn 100

From a pack of $52$ playing cards, face cards and tens are removed and kept aside then a card is drawn at random from the remaining cards. If
$A$ : The event that the card drawn is an ace
$H$ : The event that the card drawn is a heart
$S$ : The event that the card drawn is a spade

then which of the following holds?

50% studentsanswered this correctly

Important Questions on Probability

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-2>Q 22

Before a race the chance of three runners

A, B

C

were estimated to be proportional to

5, 3 & 2

respectively but during the race

A

meets with an accident which reduces his chance to

\frac{1}{3}

. If the respective chances of

B

and

C

are

P (B)

and

P (C)

then -

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-2>Q 23

E

and

F

are events with

P (E) \leq P (F)

and

P (E \cap F) > 0

, then

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Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-2>Q 24

A

and

B

are two independent events such that

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

and

P (B) = \frac{1}{5}

, then

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-3>Q 12

In a knockout tournament

2^{n}

equally skilled players;

S_{1}, S_{2} . . . . . . . . S_{2^{n}}

are participating. In each round players are divide in pair at random and winner from each pair moves in the next round. If

S_{2}

reaches the semifinal then the probability that

S_{1}

wins the tournament is

\frac{1}{20}

. Find the value of '

n

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-3>Q 13

In a multiple choice question there are four alternative answers of which one or more than one is correct. A candidate will get marks on the question only if he ticks all the correct answers. The candidate ticks the answers at random. If the probability of the candidate getting marks on the question is to be greater than or equal to

\frac{1}{3}

, then find the least number of chances he should be allowed.

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Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-3>Q 14

All the face cards from a pack of

52

playing cards are removed. From the remaining pack half of the cards are randomly removed without looking at them and then randomly drawn two cards simultaneously from the remaining. If the probability that, two cards drawn are both aces, is

\frac{p ({}^{38}C_{20})}{{}^{40}C_{20} . {}^{20}C_{2}}

, then find the value of

p

EASY

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-3>Q 15

An unbiased normal coin is tossed ' $n$ ' times

Let $E_{1} :$ event that the both Heads and Tails are present in ' $n$ ' tosses.

$E_{2} :$ event that the coin shows up Heads atmost once.

Find the value of ' $n$ ' for which $E_{1}$ and $E_{2}$ are independent.

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Beta Question Bank for Engineering: Mathematics>Chapter 11 - Probability>EXERCISE-3>Q 16

Four people sit around a circular table, and each person will roll a normal six side die once. The probability that no two people sitting next to each other will roll the same number is

\frac{N}{1296}

. Find the value of

N .

Important Questions on Probability

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