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 2

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Two dice are thrown simultaneously and three events $A, B$ and $C$ are defined as

$A :$ The sum of the numbers is $10$

$B :$ The sum of the numbers is $9$

$C :$ The sum of the numbers is $8$

If $P (E)$ is the probability of event $E$ , then which of the followings is true?

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Important Questions on Probability

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

If a coin is tossed four times then the probability that head appears at least once is

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

Two dice are thrown simultaneously and the sum of the numbers is noted. If the sum of the numbers is

7

, then the probability is

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

One card is drawn from

52

playing card. The probability that this will be red card or a King is

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

A number of four digits is selected. If the probability that number has non-repeated digits is

P

then the value of

125 P

is

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

Three dice are thrown simultaneously. If the probability that numbers on them are same is

P

, then the value of

36 P

is

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

If

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

and

P (A \cap B) = \frac{1}{3}

then the probability that

A

happens but

B

does not happen is

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Gamma Question Bank for Engineering Mathematics>Chapter 8 - Probability>Assignment>Q 9

Three students Ram, Ali and John appear at a competitive examinations. The probability of Ram comes first is thrice that of Ali and the probability of Ali coming first is thrice of John. The probability of John coming first is

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Gamma Question Bank for Engineering Mathematics>Chapter 8 - Probability>Assignment>Q 11

Given two events are