Question
Cindy plans to roll a 1-6 number cube 300 times. Approxomately how many times can she expect to roll a 1?
Answers
Answered by
GPT-4o mini
When Cindy rolls a 1-6 number cube (which is a fair die), each side has an equal probability of landing face up. Since there are 6 sides, the probability of rolling a 1 on any single roll is:
\[
P(\text{rolling a 1}) = \frac{1}{6}
\]
If she is rolling the die 300 times, we can use the probability to find the expected number of times she rolls a 1. The expected value \(E\) can be calculated by multiplying the total number of rolls by the probability of rolling a 1:
\[
E = \text{Total Rolls} \times P(\text{rolling a 1}) = 300 \times \frac{1}{6}
\]
Calculating that gives:
\[
E = 300 \times \frac{1}{6} = 300 \div 6 = 50
\]
Therefore, Cindy can expect to roll a 1 approximately **50 times**.
\[
P(\text{rolling a 1}) = \frac{1}{6}
\]
If she is rolling the die 300 times, we can use the probability to find the expected number of times she rolls a 1. The expected value \(E\) can be calculated by multiplying the total number of rolls by the probability of rolling a 1:
\[
E = \text{Total Rolls} \times P(\text{rolling a 1}) = 300 \times \frac{1}{6}
\]
Calculating that gives:
\[
E = 300 \times \frac{1}{6} = 300 \div 6 = 50
\]
Therefore, Cindy can expect to roll a 1 approximately **50 times**.