Question

What is the probability of rolling two six-sided dice and obtaining either an odd total or a total less than six?

Answer 1

Answer 2

To find the probability of rolling two six-sided dice and obtaining either an odd total or a total less than six, we need to consider all the possible outcomes and count the favorable outcomes that meet the given conditions.

There are 6 sides on each die, and the total number of outcomes when rolling two dice is 6 * 6 = 36.

Now, let's find the favorable outcomes:

Odd Totals: There are three odd totals possible: 3, 5, and 7.

To get a total of 3, you need to roll a 1 and a 2, or a 2 and a 1. (2 favorable outcomes)

To get a total of 5, you need to roll a 1 and a 4, a 2 and a 3, a 3 and a 2, or a 4 and a 1. (4 favorable outcomes)

To get a total of 7, you need to roll a 1 and a 6, a 2 and a 5, a 3 and a 4, a 4 and a 3, a 5 and a 2, or a 6 and a 1. (6 favorable outcomes)

So, there are a total of 2 + 4 + 6 = 12 favorable outcomes for obtaining an odd total.

Totals Less Than Six: To get a total less than six, the only possible outcomes are:

Rolling a 1 and a 1 (1 favorable outcome)

Rolling a 1 and a 2, or a 2 and a 1 (2 favorable outcomes)

Rolling a 1 and a 3, a 2 and a 2, or a 3 and a 1 (3 favorable outcomes)

Rolling a 1 and a 4, a 2 and a 3, or a 3 and a 2, or a 4 and a 1 (4 favorable outcomes)

Rolling a 1 and a 5, a 2 and a 4, a 3 and a 3, or a 4 and a 2, or a 5 and a 1 (5 favorable outcomes)

So, there are a total of 1 + 2 + 3 + 4 + 5 = 15 favorable outcomes for obtaining a total less than six.

Now, we need to count the total number of favorable outcomes (outcomes that meet either of the given conditions):

Total Favorable Outcomes = 12 (odd totals) + 15 (totals less than six) = 27

Finally, we can calculate the probability:

Probability = (Total Favorable Outcomes) / (Total Number of Outcomes) = 27 / 36 = 3/4 ≈ 0.75

So, the probability of rolling two six-sided dice and obtaining either an odd total or a total less than six is approximately 0.75 or 75%.