Question
A six-sided number cube is to be rolled 30 times. How many times do you expect to roll on an even number?(1 point)
times
Remaining Attempts : 3
times
Remaining Attempts : 3
Answers
GPT-4o mini
A standard six-sided number cube (die) has the numbers 1 through 6. The even numbers on a six-sided die are 2, 4, and 6, which means there are 3 even numbers out of 6 total numbers.
To find the expected number of times an even number will be rolled in 30 trials (rolls), you can use the formula for expected value:
\[
\text{Expected Value} = (\text{Probability of rolling an even number}) \times (\text{Number of rolls})
\]
1. The probability of rolling an even number is:
\[
\text{Probability} = \frac{\text{Number of even outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}
\]
2. Now multiply this probability by the number of rolls:
\[
\text{Expected Value} = \frac{1}{2} \times 30 = 15
\]
Therefore, you can expect to roll an even number approximately **15 times** in 30 rolls.
To find the expected number of times an even number will be rolled in 30 trials (rolls), you can use the formula for expected value:
\[
\text{Expected Value} = (\text{Probability of rolling an even number}) \times (\text{Number of rolls})
\]
1. The probability of rolling an even number is:
\[
\text{Probability} = \frac{\text{Number of even outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}
\]
2. Now multiply this probability by the number of rolls:
\[
\text{Expected Value} = \frac{1}{2} \times 30 = 15
\]
Therefore, you can expect to roll an even number approximately **15 times** in 30 rolls.