Probability

Discrete Probability

Uniform Probability

         

A die is made from a regular icosahedron so that each side labelled by a number from 11 through 10,10, with some labels appearing multiple times. If the the probability that it lands on the number 88 is 15,\frac{1}{5}, how many sides are labelled 8?8?

Details and assumptions

A regular icosahedron has 2020 faces.

A dartboard is equally divided into fan-shaped sectors, each with a central angle of 20.20 ^\circ. If exactly one of the sectors is painted red and a dart has equal probability of hitting every position in the dartboard, then the probability that the dart hits the red sector can be expressed as ab\frac{a}{b}, where aa and bb are coprime positive integers. What is a+b?a+b?

Details and assumptions

Assume that the dart never misses the dartboard.

A dartboard is equally divided into fan-shaped sectors, each with a central angle of 66 ^\circ, and exactly one of the sectors is painted red. If the dart has equal probability of hitting every position in the dartboard, what is the probability that it hit the red sector?

Details and assumptions

Assume that the dart never misses the dartboard.

Sophia rolls a fair standard 6-sided die with sides labeled 11 through 66. What is the probability that she rolls a 66?

Details and assumptions

In a fair die, each side is equally likely to be rolled.

A magician randomly draws one card from a standard 5252 card deck. The probability that the card drawn is a heart or a diamond can be written as ab\frac{a}{b}, where aa and bb are positive, coprime integers. What is the value of a+ba+b?

Details and assumptions

A standard deck of cards consists of 52 cards, formed by 13 ranks (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q and K) of 4 suits (clubs, diamonds, hearts and spades).

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