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 33

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$A, B$ 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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Important Questions on Probability

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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

a

and

b

are chosen at random from the set of integers

1, 2, 3, \dots . 15

. The probability that the equation

2 a - 3 b = 0

is satisfied, is

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Gamma Question Bank for Engineering Mathematics>Chapter 8 - Probability>Assignment>Q 4

Let

n = 2^{3} 4^{5} 6^{8} 5^{4}

. A positive factor is taken at random from the possible positive factors of

n

. Then the probability that the selected factor is a perfect square and divisible by

100

is

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Gamma Question Bank for Engineering Mathematics>Chapter 8 - Probability>Assignment>Q 5

Dialling a telephone number an old man forgets the last two digits remembering only that these are different dialled at random. The probability that the number is dialled correctly is

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Gamma Question Bank for Engineering Mathematics>Chapter 8 - Probability>Assignment>Q 6

There are four balls of different colours and four boxes of colours same as of the balls. The probability to place the balls, one in each box, such that a ball does not go to a box of its own colour, is

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Gamma Question Bank for Engineering Mathematics>Chapter 8 - Probability>Assignment>Q 7

Four digit number is formed from all possible ways. The probability that a number