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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Q. Suppose a rectangle edges equals i = 4.7 and j = 8.3. Now, a straight line drawn through randomly selected two points K and L in adjacent rectangle edges. Find the condition for the probability such that the drawn triangle area is smaller than c = 9.38.

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Q. Find the expectation for how many bacteria there are per field if there are 2350 bacteria are randomly distributed over 340 fields (all having the same size) next to each other.

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Q. What is the possibility such that the inequality x² + b > ax is true, when a=32.4 and b=76.5 and x∈[0,30].

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Q. In a bucket there are 5 purple, 15 grey and 25 green balls. If the ball is picked up randomly, find the probability that it is neither grey nor purple?

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Q. Two fair coins are flipped. As a result of this, tails and heads runs occurred where a tail run is a consecutive occurrence of at least one head. Determine the probability function of number of tail runs.

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