To find how many times Tamara can expect the sum of the two number cubes to be equal to 7 when she rolls the cubes 144 times, we first need to determine the probability of rolling a sum of 7.
When rolling two number cubes (also known as dice), the possible sums can range from 2 (1+1) to 12 (6+6). Here are the combinations that yield a sum of 7:
- (1, 6)
- (2, 5)
- (3, 4)
- (4, 3)
- (5, 2)
- (6, 1)
There are 6 successful outcomes that result in a sum of 7.
Since there are a total of 36 possible combinations (6 faces on the first die multiplied by 6 faces on the second die), the probability \( P \) of rolling a sum of 7 is calculated as follows:
\[ P(\text{sum} = 7) = \frac{\text{number of successful outcomes}}{\text{total outcomes}} = \frac{6}{36} = \frac{1}{6} \]
Next, to find the expected number of times the sum will be 7 in 144 rolls, we multiply the total number of rolls by the probability:
\[ \text{Expected times} = 144 \times P(\text{sum} = 7) = 144 \times \frac{1}{6} \]
Calculating this gives:
\[ \text{Expected times} = 144 \div 6 = 24 \]
Thus, Tamara should expect the sum of the two cubes to be equal to 7 about 24 times if she rolls the two number cubes 144 times.