Answer :
To predict how many times you would expect to roll the number 3 when you roll a six-sided number cube a total of 200 times, follow these steps:
1. Determine the Total Number of Rolls:
- You are rolling the number cube 200 times.
2. Calculate the Probability of Rolling a 3:
- Since the cube is fair and has 6 sides, each number (1 through 6) has an equal probability of being rolled.
- The probability of rolling a 3 is [tex]\(\frac{1}{6}\)[/tex].
3. Calculate the Expected Number of Times to Roll a 3:
- The expected number of times to roll a specific number can be found by multiplying the total number of rolls by the probability of rolling that number.
- Therefore, the expected number of times to roll a 3 is calculated as:
[tex]\[ 200 \text{ rolls} \times \frac{1}{6} = 33.3333 \text{ times} \][/tex]
Thus, the expected number of times you would roll a 3 is approximately [tex]\(33.3333\)[/tex].
Given the options provided:
- About 17
- About 25
- About 33
- About 66
The correct answer is "about 33".
1. Determine the Total Number of Rolls:
- You are rolling the number cube 200 times.
2. Calculate the Probability of Rolling a 3:
- Since the cube is fair and has 6 sides, each number (1 through 6) has an equal probability of being rolled.
- The probability of rolling a 3 is [tex]\(\frac{1}{6}\)[/tex].
3. Calculate the Expected Number of Times to Roll a 3:
- The expected number of times to roll a specific number can be found by multiplying the total number of rolls by the probability of rolling that number.
- Therefore, the expected number of times to roll a 3 is calculated as:
[tex]\[ 200 \text{ rolls} \times \frac{1}{6} = 33.3333 \text{ times} \][/tex]
Thus, the expected number of times you would roll a 3 is approximately [tex]\(33.3333\)[/tex].
Given the options provided:
- About 17
- About 25
- About 33
- About 66
The correct answer is "about 33".
