Math Problem Statement

A biased dice is thrown thirty times and the number of sixes seen is eight.

If the dice is thrown a further twelve times, find the probability that a six will occur exactly twice.

The answer is rounded up to 4 decimal places.

0.2111

0.2222

0.2099

0.2345

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Binomial Distribution

Formulas

Binomial probability formula: P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
Empirical probability: p = number of successes / number of trials

Theorems

Binomial Theorem

Suitable Grade Level

Grades 10-12