Calculate Probability and Statistics for Dice Roll Outcomes

Q: Calculate Probability and Statistics for Dice Roll Outcomes

This question evaluates understanding of discrete probability and the Binomial distribution, specifically computing point probabilities, expected value, and standard deviation for count data.

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Question

Dice Rolls and the Binomial Model

Scenario

A casino analyst models dice rolls to understand outcome probabilities for marketing promotions.

Question

You roll a fair six-sided die 10 times. Let X be the number of sixes observed.

Compute:

P(X = 3) — the probability of observing exactly 3 sixes.
E[X] — the expected number of sixes in 10 rolls.
SD[X] — the standard deviation of the number of sixes.

Hint: Model X with a Binomial distribution: n = 10, p = 1/6.

Calculate Probability and Statistics for Dice Roll Outcomes

Dice Rolls and the Binomial Model

Scenario

Question

Solution

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