What is the probability that a leap year, selected at random will contain 53 Sundays?

A leap year has 366 days = 52 weeks + 2 days . That 2 days can be Sunday-Monday, Monday-Tuesday, Tuesday-Wednesday, Wednesday-Thursday,..., Saturday-Sunday. Total outcomes = 7 (Sun-Mon, Mon-Tue, Tue-Wed, Wed-Thu, Thu-Fri, Fri-Sat, Sat-Sun) Number of favourable outcomes i.e, Sunday, n E = 2 n S = 7 Required probability, P E = n E n S = 2 7

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Gamma Question Bank for Engineering Mathematics>Chapter 8 - Probability>Assignment>Q 28

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Two distinct numbers are selected at random from the first twenty natural numbers. The probability that the sum will be divisible by $3$ is $\frac{p}{q}$ , where $p, q$ are coprime then $(p + q)$ is equal to

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Important Questions on Probability

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Gamma Question Bank for Engineering Mathematics>Chapter 8 - Probability>Assignment>Q 29

Three numbers

a, b

and

c

are selected from the set

\{1, 3, 5, 7, 9, 11, 13\}

then the probability that

a + b + c = 13

is

\frac{p}{q}

, where

p

and

q

are coprime then

p + q

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 8 - Probability>Assignment>Q 30

Out of all possible numbers formed by using all the digits

1, 2, 3, 4, 3, 2, 1

. A number is selected then the probability that selected number has its odd digits at odd places is

\frac{1}{N}

, then

N

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 8 - Probability>Assignment>Q 31

Out of all positive integral divisors of

240

one of them is selected then the probability that it is in the form

4 n + 2, (n \geq 0)

is

\frac{1}{N}

then

N

is

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Gamma Question Bank for Engineering Mathematics>Chapter 8 - Probability>Assignment>Q 32

If four squares are chosen at random on a chess board. If the probability that they lie on a diagonal line is

P

then

158844 P

is

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Gamma Question Bank for Engineering Mathematics>Chapter 8 - Probability>Assignment>Q 33

A, B

and

C

, play a game and chances of their winning it in an attempt are

\frac{2}{3}, \frac{1}{2}

and

\frac{1}{4}

, respectively.

A

, has the first chance followed by

B

, and then by

C

. This is repeated till one of them wins the game. Let

x, y, z

, are their respective chances of winning the game, then

\frac{x}{z}

, is

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Gamma Question Bank for Engineering Mathematics>Chapter 8 - Probability>Assignment>Q 1

If

P (A) = \frac{1}{2}, P (B) = \frac{2}{5}, P (C) = \frac{1}{2}

and

P (A \cap B) = P (B \cap C) = P (C \cap A) = \frac{1}{4}

and

P (A \cap B \cap C) = \frac{1}{8}

then the probability that at least one of them appears is

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Gamma Question Bank for Engineering Mathematics>Chapter 8 - Probability>Assignment>Q 2

In a game of six digits, two digits are already fixed for prize. If anyone will find these two fixed digits then he will win the prize. Mr. A selects two numbers. The probability that Mr. A will win the prize is

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Gamma Question Bank for Engineering Mathematics>Chapter 8 - Probability>Assignment>Q 3

Two numbers