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Probability

Counting, expectation, fair games.

ProbabilityCounting★☆☆☆☆Easy+20 XP

A fair six-sided die is rolled once. What is the probability of an even number? (Fraction in lowest terms.)

ProbabilityCounting★☆☆☆☆Easy+20 XP

A bag holds 3 red and 5 blue marbles. One is drawn at random. What is the probability it is red? (Fraction.)

ProbabilityCounting★☆☆☆☆Easy+20 XP

Two fair coins are flipped. What is the probability both land heads? (Fraction.)

ProbabilityCounting★★☆☆☆Medium+30 XP

A spinner has 8 equal sections numbered 1–8. What is the probability of landing on a number greater than 6? (Fraction.)

ProbabilityCounting★★☆☆☆Medium+30 XP

Two fair six-sided dice are rolled. What is the probability the sum is 7? (Fraction in lowest terms.)

ProbabilityCounting★☆☆☆☆Easy+20 XP

What is the probability of NOT rolling a 6 on one fair die? (Fraction.)

ProbabilityConditional probability★★★☆☆Hard+40 XP

A bag has 4 red and 6 blue marbles. Two are drawn without replacement. What is the probability both are red? (Fraction in lowest terms.)

ProbabilityCounting★★☆☆☆Medium+30 XP

How many different arrangements are there of the letters in MATH?

ProbabilityCounting★★★☆☆Hard+40 XP

How many ways are there to choose 3 students from a group of 10?

ProbabilityCounting★★★☆☆Hard+40 XP

A fair coin is flipped 3 times. What is the probability of at least one head? (Fraction.)

ProbabilityExpected value★★☆☆☆Medium+30 XP

What is the expected value of a single roll of a fair six-sided die? (Fraction.)

ProbabilityConditional probability★★★☆☆Hard+40 XP

From 5 boys and 4 girls, two people are chosen at random. What is the probability both are girls? (Fraction.)

ProbabilityExpected value★★☆☆☆Medium+30 XP

What is the expected number of heads in 10 flips of a fair coin?

Premium problem

A fair coin is flipped 4 times. What is the expected number of times a flip differs from the one before it? (Fraction.)

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ProbabilityProbability games★★★☆☆Hard+40 XP

A fair coin is flipped 4 times. What is the probability of exactly 2 heads? (Fraction in lowest terms.)

Premium problem

Three fair dice are rolled. What is the probability that all three show different numbers? (Fraction in lowest terms.)

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Premium problem

In how many ways can 4 letters be placed into 4 addressed envelopes so that no letter goes into its correct envelope?

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