Lesson Probability of Rolling at Least 10

Source code of 'Probability of Rolling at Least 10'

This Lesson (Probability of Rolling at Least 10) was created by by oberobic(2304)

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<b>Problem:</b>  With a pair of fair dice, what is the probability that a single roll will have a total of at least 10?
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<b>Solution:</b>  Probability always is based on the number of favorable outcomes divided by the total possible outcomes.  With 2 dice there are 36 possible outcomes for any roll:  6*6 =36.  The following table shows the possible sums:
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<TABLE border="3">
<tr><th><th colspan="7">Die 1</tr>
<tr><th rowspan="8">Die 2</tr>
<tr><th>&nbsp;&nbsp;&nbsp;<th>1&nbsp;&nbsp;&nbsp;<th>2&nbsp;&nbsp;&nbsp;<th>3&nbsp;&nbsp;&nbsp;<th>4&nbsp;&nbsp;&nbsp;<th>5&nbsp;&nbsp;&nbsp;<th>6&nbsp;&nbsp;&nbsp;</tr>
<tr><th>1&nbsp;&nbsp;&nbsp;<td>2<td>3<td>4<td>5<td>6<td>7</tr>
<tr><th>2&nbsp;&nbsp;&nbsp;<td>3<td>4<td>5<td>6<td>7<td>8</tr>
<tr><th>3&nbsp;&nbsp;&nbsp;<td>4<td>5<td>6<td>7<td>8<td>9</tr>
<tr><th>4&nbsp;&nbsp;&nbsp;<td>5<td>6<td>7<td>8<td>9<td>10</tr>
<tr><th>5&nbsp;&nbsp;&nbsp;<td>6<td>7<td>8<td>9<td>10<td>11</tr>
<tr><th>6&nbsp;&nbsp;&nbsp;<td>7<td>8<td>9<td>10<td>11<td>12</tr>
</table>

The question is what is the probability the sum is at least 10. Inspecting this table, you can see that:
1 of these 36 outcomes = 12
2 of these 36 outcomes = 11
3 of these 36 outcomes = 10 
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<b>Answer:</b>  The probability that the sum will be 10 or more is:
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P(10 or more) = 6/36 = 1/6
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This result may be expressed as about 16.67%.