Q. In a secondary examination, 75% of the students have passed in History and 65% in Mathematics, while 50% passed in both History and Mathematics. If 35 candidates failed in both the subjects, what is the total number of candidates sit for that exam?

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Q. In a Press Conference, there are 450 foreign journalists. 275 people can speak German, 250 people can speak English, 200 people can speak Chinese and 260 people can speak Japanese. Find the maximum number of foreigners who cannot speak at least one language.

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Q. There is a class of 40 students out of which 16 are girls. There are 27 students who are right-handed. How many minimum numbers of girls who are left-handed in this class?

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Q. How many positive integers less than or equal to 100 are divisible by 2, 4 or 5?

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Q. How many ways are there to select exactly four clocks from a store with 10 wall-clocks and 16 stand-clocks?

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Q. If a 12-sided fair die is rolled twice, find the probability that both rolls have a result of 8.

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Q. How many positive divisors does 4000 = 2⁵ 5³ have?

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Q. Mina has 6 different skirts, 3 different scarfs and 7 different tops to wear. She has exactly one orange scarf, exactly one blue skirt, and exactly one black top. If Mina randomly selects each item of clothing, find the probability that she will wear those clothings for the outfit.

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Q. There are 6 possible routes (1, 2, 3, 4, 5, 6) from Chennai to Kochi and 4 routes (7, 8, 9, 10) from the Kochi to the Trivendrum. If each path is chosen at random, what is the probability that a person can travel from the Chennai to the via the 4th and 9th road?

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Q. If two 14-sided dice one is red and one is blue are rolled, find the probability that a 3 on the red die, a 5 on the blue die are rolled.

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Q. Suraj wants to go to Delhi. He can choose from bus services or train services to downtown Punjab. From there, he can choose from 4 bus services or 7 train services to head to Delhi. The number of ways to get to Delhi is?

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Q. Two cards are chosen at random from a standard deck of 52 playing cards. What is the probability of selecting a jack and a Spade from the deck?

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Q. If I throw 3 standard 7-sided dice, what is the probability that the sum of their top faces equals to 21? Assume both throws are independent to each other.

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Q. A box consists of 5 yellow, 12 red and 8 blue balls. If 5 balls are drawn from this box one after the other without replacement, find the probability that the 5 balls are all yellow balls.

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Q. Suppose, R is a random real number between 5 and 9. What is the probability R is closer to 5 than it is to 6?

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Q. A ball is thrown at a circular bin such that it will land randomly over the area of the bin. Find the probability that it lands closer to the center than to the edge?

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Q. A programmer has a 95% chance of finding a bug every time she compiles his code, and it takes her three hours to rewrite the code every time she discovers a bug. Find the probability that she will finish her program by the end of her workday. (Assume that a workday is 9 hours)

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Q. A football player has a 45% chance of getting a hit on any given pitch. What is the probability that the player earns a hit ignoring the balls before he strikes out (that requires four strikes)?

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Q. What is variance of a geometric distribution having parameter p=0.72?

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Q. The probability that it rains tomorrow is 0.72. Find the probability that it does not rain tomorrow?

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