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?
a. binomial probability; ( n = 12 ), ( p=\frac{1}{6} ), ( q=\frac{5}{6} )
b. binomial probability; ( n = 12 ), ( p=\frac{1}{12} ), ( q=\frac{11}{12} )
c. binomial probability; ( n = 100 ), ( p=\frac{1}{6} ), ( q=\frac{5}{6} )
d. not a binomial probability
please select the best answer from the choices provided

Explanation:

Step1: Check binomial conditions

A binomial experiment has \(n\) independent trials. Here, rolling a pair of dice \(100\) times (\(n = 100\)) are independent trials.

Step2: Define success and failure

Success is getting doubles. When rolling a pair of dice, there are \(6\) ways to get doubles \((1 - 1,2 - 2,\cdots,6 - 6)\) out of \(36\) possible outcomes. So \(p=\frac{6}{36}=\frac{1}{6}\).

Step3: Calculate \(q\)

Since \(q=1 - p\), then \(q = 1-\frac{1}{6}=\frac{5}{6}\)

Answer:

C. Binomial probability; \(n = 100\), \(p=\frac{1}{6}\), \(q = \frac{5}{6}\)