Question

In the following experiment, determine whether or not the probabilities are binomial probabilities. If they are, identify the values for n, p, and q. A pair of dice are rolled 100 times. What is the probability of getting doubles x times?

Answer 1

Answer: C. Binomial Probability; n=12, p=1/12, q= 11/12

Explanation:

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Answer 2

Assuming the dice rolls are independent, the probability of getting doubles is
`\dbinom61\frac16\cdot\frac16=\frac6{36}=\frac16`. (That is, there are 6 ways of getting doubles, and the probability of getting a given face is 1/6.)

So the event of getting doubles in a set number of
`n` trials is binomially distributed with
`p=\frac16` (and so
`q=1-p=\frac56`).

You're given that
`n=100`. If
`X` is a random variable representing the number of doubles obtained in
`n` trials, then the probability of getting
`X=x` doubles is given by the PMF,


`\mathbb P(X=x)=\begin{cases}\dbinom{100}x\frac16^x\cdot\left(\frac56\right)^(100-x)&\text{for }0\le x\le100\\\\0&\text{otherwise}\end{cases}`