Question

john is about to roll a six - sided, fair number cube 60 times. he wants to predict how many times the cube will land on an even number. he makes a prediction of 20 times. is it a good prediction? what would your prediction be based on theoretical probability?

Explanation:

Step1: Determine probability of even number

A six - sided cube has numbers 1, 2, 3, 4, 5, 6. The even numbers are 2, 4, 6, so there are 3 even numbers out of 6 total. The probability of rolling an even number, $P(\text{even})=\frac{3}{6}=\frac{1}{2}$.

Step2: Calculate expected number of even rolls

John rolls the cube 60 times. The expected number of times an even number is rolled is the number of trials times the probability of the event. So we calculate $60\times\frac{1}{2}=30$.

John's prediction of 20 is not a good prediction because the theoretical probability - based prediction is 30.

Answer:

30