Math Problem Statement

A fair six-sided die is rolled six times. Which of the following is/are given by (6 choose 2) (1/6)^2 (5/6)^4?

Solution

Thank you for uploading the file! Let me know which specific question you'd like help with, and I’ll provide solutions or explanations.

Here are a few options to consider:

  1. Question 1: Probability using a fair six-sided die and combinations.
  2. Question 3: Finding the minimum number of trials for a success probability greater than 0.99.
  3. Question 4: Probability of more girls than boys in a family of six children.
  4. Question 6: Solving for a constant kk and calculating probabilities with a biased die.
  5. Question 7: Calculating probabilities related to Mr. Bullar’s car parking habits.

Let me know which one to start with or if you need solutions for all!

Here’s a tip:
When tackling probability problems involving binomial distributions, remember the formula:
P(X=r)=(nr)pr(1p)nrP(X = r) = \binom{n}{r} p^r (1-p)^{n-r}
where nn is the number of trials, pp is the probability of success, and rr is the desired number of successes.

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Math Problem Analysis

Mathematical Concepts

Probability
Combinatorics
Binomial Distribution

Formulas

Binomial Probability Formula: P(X = r) = nCr * p^r * (1-p)^(n-r)
Combination Formula: nCr = n! / (r!(n-r)!)

Theorems

Binomial Theorem

Suitable Grade Level

Grades 10-12