if you roll a 6 - sided die 6 times, what is the best prediction possible for the number of times you will…
if you roll a 6 - sided die 6 times, what is the best prediction possible for the number of times you will roll an even number? times
Answer
Explanation:
Step1: Determine probability of rolling even
On a 6 - sided die, even numbers are 2, 4, 6. So there are 3 even numbers out of 6. The probability $P$ of rolling an even number in a single roll is $P=\frac{3}{6}=\frac{1}{2}$.
Step2: Use expected - value formula
The expected - value formula for a binomial experiment is $E = n\times p$, where $n$ is the number of trials and $p$ is the probability of success in a single trial. Here, $n = 6$ (number of rolls) and $p=\frac{1}{2}$ (probability of rolling an even number). So $E=6\times\frac{1}{2}$.
Step3: Calculate the result
$6\times\frac{1}{2}=3$.
Answer:
3