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An urn contains 3 red, 2 blue and 5 white balls. A ball is selected and its colour is noted. Then it is replaced with a black ball. A second ball is selected and placed back into the urn after colour is noted. If the second ball is a black ball, three purple will be added into the urn. If the second ball is not a black ball, ten white balls will be added. If the second ball is a red or blue, five black balls will be added. Then, a third ball will be selected. Find the probability of getting black ball in third selection if second ball is a red ball.

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There are 35 people in a room, what is the probability that at least 2 people have the same birthday? Assume that birthdays are uniformly distributed and there is no leap year complication.

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We didnt cover cumulative distribution function in our syllabus. Basically to get F(t) from f(t), we integrate. To get f(t) from F(t), we differentiate. 

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Please refer to the next post for the question.

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Consider all the six digit numbers that can be formed using digits 1, 2, 3, 4, 5 and 6, each digit being used exactly once. How many six digit numbers have the property such that the number is divisible by the digit at its unit place?
A) 624
B) 648
C) 672
D) 720

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Consider all the six digit numbers that can be formed using digits 1, 2, 3, 4, 5 and 6, each digit being used exactly once. How many six digit numbers have the property such that the number is divisible by the digit as its unit place?
A) 624
B) 648
C) 672
D) 720

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A set of positive integers from 1 to 55 (inclusive) where each integer only appears once in the set are placed in 11 groups of 5 each. What is the difference between the largest possible median and smallest possible median of these 11 groups?
A) 50
B) 54
C) 52
D) The provided information is insufficient.

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Set S contains 7 distinct integers. The median and the largest integer in the set is m and 3m respectively. What is the range of the set when the possible mean of the set is highest?
A) 2m-1
B) 2m-2
C) 2m+3
D) 2m+4

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A manufacturer claims that only 1.5% of bulbs produced are defective. An inspection process consists of testing four sets which has 8 bulbs in each set. If more than two sets have at most one defective bulbs in each set, then a purchase will be made. What is the percentage that purchase will be made?

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When a biased six-faced die is tossed, the probability of getting an even number is 2 times higher than the probability of getting an odd number. The die is tossed seven times and the outcomes are recorded. What is the probability that the sum of the seven outcomes is an odd number?

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In an experiment, three balls are selected at random without replacement from a box containing 4 red balls and 6 black balls. The experiment is repeated for 100 times. Throughout the procedure, how many red balls are expected to be selected?

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An electronic factory is supplied with 750 microchips. To determine if the microchip supplied are in good condition, 20 microchips are selected at random and inspected. If none or only one of the microchip is defective, then the supply of 750 microchips will be accepted.
Suppose that the entire supply of 750 microchips contains 37 defective microchips. Find the probability that the supply will be accepted entirely and the probability that exactly one microchip will be found to be defective if it is known that the entire supply has been accepted.