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. based on theoretical probability, which best describes johns prediction?

Explanation:

Step1: Calculate the theoretical probability of rolling an even number

A six - sided cube has numbers \(1,2,3,4,5,6\). The even numbers are \(2,4,6\). So there are \(n = 3\) favorable outcomes and \(N=6\) total outcomes. The probability \(P=\frac{n}{N}=\frac{3}{6}=\frac{1}{2}\).

Step2: Use the formula for expected value

The formula for the expected value \(E\) (when the number of trials is \(n = 60\)) is \(E=n\times P\). Substitute \(n = 60\) and \(P=\frac{1}{2}\) into the formula: \(E = 60\times\frac{1}{2}=30\).

Answer:

John's prediction is low, because \(60(\frac{1}{2})=30\).