john is about to roll a six - sided, fair number cube 60 times. he wants to predict how many times the cube…

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?

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?

Answer

Explanation:

Step1: Find 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 expected number of times

The die is rolled $n = 60$ times. Using the formula for expected value $E=n\times P$, we substitute $n = 60$ and $P=\frac{1}{2}$. So $E=60\times\frac{1}{2}=30$.

Answer:

No, it is not a good prediction. Based on theoretical probability, the prediction should be 30 times.