To solve this problem, we need to predict the number of times Terry will roll a number greater than 4 on a number cube that is numbered from 1 to 6 when she rolls the cube 50 times.
Step-by-Step Solution:
1. Identify the Favorable Outcomes:
- The numbers on the cube are {1, 2, 3, 4, 5, 6}.
- The numbers greater than 4 are 5 and 6.
- So, the favorable outcomes are 5 and 6, which gives us 2 favorable outcomes.
2. Calculate the Total Number of Outcomes:
- A number cube has 6 faces.
- Therefore, there are 6 possible outcomes in total.
3. Determine the Probability of Rolling a Number Greater than 4:
- The probability [tex]\( P(\text{number greater than 4}) \)[/tex] is the ratio of the number of favorable outcomes to the total number of outcomes.
- Thus, [tex]\( P(\text{number greater than 4}) = \frac{2}{6} \)[/tex].
4. Calculate the Expected Number of Favorable Rolls:
- Terry rolls the cube 50 times.
- The expected number of times she will roll a number greater than 4 is given by [tex]\( \text{Probability} \times \text{Number of rolls} \)[/tex].
- So, the equation will be [tex]\( P(\text{number greater than 4}) \times 50 = \frac{2}{6} \times 50 \)[/tex].
Hence, the correct equation to predict the number of times Terry will roll a number greater than 4 is:
[tex]\[ P(\text{number greater than 4}) = \frac{2}{6}(50) \][/tex]
Therefore, the correct choice is:
[tex]\[ P(\text{number greater than 4}) = \frac{2}{6}(50) \][/tex]
