Let's solve this problem step-by-step.
1. Probability of Rolling a Two:
First, we need to determine the probability of rolling a two on a six-sided die. A six-sided die has six faces, each showing a different number from 1 to 6. There is only one face with the number two on it. Therefore, the probability of rolling a two is:
[tex]\[
\text{Probability of rolling a two} = \frac{1}{6}
\][/tex]
2. Number of Rolls:
We are given that the die is rolled 60 times.
3. Expected Number of Twos:
To find the expected number of times a specific outcome (rolling a two, in this case) will occur, we multiply the probability of that outcome by the number of trials (rolls). So, we calculate the expected number of twos as:
[tex]\[
\text{Expected number of twos} = \left(\frac{1}{6}\right) \times 60
\][/tex]
From the calculation, we get:
[tex]\[
\text{Expected number of twos} = 0.16666666666666666 \times 60 = 10
\][/tex]
Therefore, if you roll the die 60 times, you can expect to roll a two approximately 10 times.
Answer:
You can expect to roll a two 10 times.
