A die is rolled 60 times. What is the variance of the number of times 3 is rolled?
Answer
Step 2: Find the variance. The variance of a binomial distribution is given by \(np(1 - p)\). Substituting the given values, we get \(60 * \frac{1}{6} * (1 - \frac{1}{6}) = 60 * \frac{1}{6} * \frac{5}{6} = 50/6\)
Step 1 ：Step 1: Identify the distribution. A die roll is a binomial trial, so the number of successes in 60 trials is a binomial distribution. Since a die has 6 faces and we are interested in the number of times 3 is rolled, the probability of success (rolling a 3) on each trial is \(\frac{1}{6}\). So, this is a binomial distribution with parameters n = 60 and p = \(\frac{1}{6}\).
Step 2 ：Step 2: Find the variance. The variance of a binomial distribution is given by \(np(1 - p)\). Substituting the given values, we get \(60 * \frac{1}{6} * (1 - \frac{1}{6}) = 60 * \frac{1}{6} * \frac{5}{6} = 50/6\)
