Terry has a number cube that is numbered from 1 to 6. She rolls the cube 50 times. Which equation can be used to predict the number of times that she will roll a number that is greater than 4?

A. [tex]P(\text{number greater than 4}) = \frac{1}{6}(50)[/tex]
B. [tex]P(\text{number greater than 4}) = \frac{2}{6}(50)[/tex]
C. [tex]P(\text{number greater than 4}) = \frac{3}{6}(50)[/tex]
D. [tex]P(\text{number greater than 4}) = \frac{5}{6}(50)[/tex]



Answer :

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]