Question

Tamara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible combinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes be equal to 7 if she rolls the two number cubes 216 ​times?
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Part 1
The sum should be equal to 7 about
  
enter your response here ​time(s).

Answer 1

To determine how many times Tamara can expect the sum of two rolled number cubes to equal 7 in 216 rolls, we first need to identify how many outcomes yield the sum of 7.

When rolling two six-sided cubes, the possible outcomes for each pair of cubes (Cube 1 and Cube 2) can be counted:

1. (1, 6)
2. (2, 5)
3. (3, 4)
4. (4, 3)
5. (5, 2)
6. (6, 1)

In total, there are 6 combinations that produce the sum of 7.

Next, we calculate the probability of rolling a sum of 7:

\[
P(\text{sum of 7}) = \frac{\text{number of outcomes that sum to 7}}{\text{total number of outcomes}} = \frac{6}{36} = \frac{1}{6}
\]

Now, if Tamara rolls the cubes 216 times, we can find the expected number of times the sum will equal 7 by multiplying the total number of rolls by the probability of rolling a sum of 7:

\[
\text{Expected times} = 216 \times P(\text{sum of 7}) = 216 \times \frac{1}{6} = 216 \div 6 = 36
\]

Hence, Tamara should expect the sum of the two cubes to equal 7 about **36 times** if she rolls the two number cubes 216 times.