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If $x$ and $y$ co-ordinates of any point $P$ are chosen randomly from intervals $[0, 2]$ and $[0, 1]$ respectively, then the probability $y \leq x^{2}$ is

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Important Questions on Probability

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Gamma Question Bank for Engineering Mathematics>Chapter 21 - Probability>Assignment>Q 49

One mapping is selected at random from all the mappings of the set

A = \{a, e, i, o, u\}

into itself. The probability that the selected one is one to one is given by

\frac{m}{n}

, where

m

and

n

are coprime then

(m + n)

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 21 - Probability>Assignment>Q 51

A

and

B

each throw a die. The probability that

A

's throw is not greater than

B

's is

\frac{p}{q}

where

p

and

q

are coprime then

p + q

is equal to

HARD

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Gamma Question Bank for Engineering Mathematics>Chapter 21 - Probability>Assignment>Q 52

An urn contains

2

white and

2

black balls. A ball is drawn at random. If it is white, it is not replaced into urn, otherwise it is replaced along with another ball of the same colour. The process is repeated. If the probability that third ball drawn is black is

\frac{p}{q}

, where

p

and

q

are coprime then

p + q

must be

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Gamma Question Bank for Engineering Mathematics>Chapter 21 - Probability>Assignment>Q 53

A biased coin with probability

P, 0 < P < 1

of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is

\frac{1}{6}

then,

P = \frac{m}{n}

, where

m

and

n

are coprime then

n^{m}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 21 - Probability>Assignment>Q 1

A coin is tossed three times in succession. If

E

is the event that there are at least two heads and

F

is the event in which first throw is a head, then

P (E | F)

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 21 - Probability>Assignment>Q 2

\bar{E}

and

\bar{F}

are the complementary events of events

E

and

F

respectively and if

0 < P (F) < 1

, then

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Gamma Question Bank for Engineering Mathematics>Chapter 21 - Probability>Assignment>Q 3

Three dice, each numbered

1

6

are rolled. One die is fair and others are biased so that for each of them a six is twice as likely to occur as any other score. One of the dice is chosen at random and on two throws it shows a six on each occasion. The probability that the die chosen was biased is

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Gamma Question Bank for Engineering Mathematics>Chapter 21 - Probability>Assignment>Q 4

If three dice are thrown together, then the probability of getting

5

on at least one of them is

If x and y co-ordinates of any point P are chosen randomly from intervals 0,2 and 0,1 respectively, then the probability y≤x2 is

Important Questions on Probability

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If $x$ and $y$ co-ordinates of any point $P$ are chosen randomly from intervals $[0, 2]$ and $[0, 1]$ respectively, then the probability $y \leq x^{2}$ is