To calculate the probability of getting a sum of 7 or 11 when you toss two number cubes, follow these steps:
1. Identify the Probabilities:
You have the probability for each possible sum as follows:
[tex]\[
P(2) = \frac{1}{36}, \quad P(3) = \frac{1}{18}, \quad P(4) = \frac{1}{12}, \quad P(5) = \frac{1}{9}, \quad
P(6) = \frac{5}{36}, \quad P(7) = \frac{1}{6}, \quad P(8) = \frac{5}{36}, \quad P(9) = \frac{1}{9}, \quad
P(10) = \frac{1}{12}, \quad P(11) = \frac{1}{18}, \quad P(12) = \frac{1}{36}
\][/tex]
2. Extract the Relevant Probabilities:
You need the probabilities for the sums of 7 and 11:
[tex]\[
P(7) = \frac{1}{6}, \quad P(11) = \frac{1}{18}
\][/tex]
3. Calculate the Combined Probability:
Since getting a sum of 7 or 11 are mutually exclusive events, you can add their probabilities to find the total probability of getting either sum.
[tex]\[
P(7 \, \text{or} \, 11) = P(7) + P(11)
\][/tex]
4. Substitute the Values:
[tex]\[
P(7 \, \text{or} \, 11) = \frac{1}{6} + \frac{1}{18}
\][/tex]
5. Find a Common Denominator and Add:
The common denominator for 6 and 18 is 18.
[tex]\[
\frac{1}{6} = \frac{3}{18}
\][/tex]
Therefore,
[tex]\[
P(7 \, \text{or} \, 11) = \frac{3}{18} + \frac{1}{18} = \frac{4}{18} = \frac{2}{9}
\][/tex]
So, the probability of getting a sum of 7 or 11 when you toss two number cubes is:
[tex]\[ \boxed{\frac{2}{9} \approx 0.2222222222} \][/tex]
In decimal form, this is approximately 0.2222, or 22.22%.
