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 die is rolled 30 times. what is the probability of getting ( x ) even numbers?
a. binomial probability; ( n = 0.5 ), ( p = 0.5 ), ( q = 30 )
b. binomial probability; ( n = 30 ), ( p = 0.5 ), ( q = 0.5 )
c. binomial probability; ( n = 0.5 ), ( p = 30 ), ( q = 0.5 )
d. not a binomial probability
please select the best answer from the choices provided
a
b
c
d

Explanation:

Step1: Check binomial conditions

A binomial experiment has \(n\) independent trials. Here, rolling a die \(30\) times (\(n = 30\)) are independent trials.

Step2: Define success and failure

Let success be getting an even number. A die has \(6\) faces (\(1,2,3,4,5,6\)). The even numbers are \(2\), \(4\), \(6\). So \(p=\frac{3}{6}=0.5\).

Step3: Calculate \(q\)

Since \(q = 1 - p\), \(q=1 - 0.5=0.5\)

Answer:

B. Binomial probability; \(n = 30\), \(p = 0.5\), \(q = 0.5\)