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 the probability of rolling an even number

On a six - sided die, the even numbers are 2, 4, 6. So there are 3 even numbers out of 6 total numbers. The probability $P$ of rolling an even number is $P=\frac{3}{6}=\frac{1}{2}$.

Step2: Calculate the expected number of times

The number of rolls is $n = 60$. The expected number of times $E$ the die lands on an even number is given by the formula $E=n\times P$. Substituting $n = 60$ and $P=\frac{1}{2}$, we get $E=60\times\frac{1}{2}=30$.

Answer:

No, it is not a good prediction. The prediction based on theoretical probability is 30 times.