Question

In a single throw of a pair of dice, find the probability of obtaining a total of 4 or less.

Short answer

The probability of obtaining a total of 4 or less in a single throw of a pair of dice is \(\frac{1}{4}\) or 25%.

Step-by-step solution

Identify the possible outcomes

A die has six faces, numbered 1 to 6. When throwing a pair of dice, there are a total of 36 possible outcomes - 6 outcomes for each die, resulting in 6 × 6 = 36 possible combinations.

Determine the favorable outcomes

Now, we will find all the combinations where the total is 4 or less. The favorable outcomes for getting a total of 4 or less are as follows: (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3) There are a total of 9 favorable outcomes.

Calculate the probability

The probability of an event is the ratio of the number of favorable outcomes to the total possible outcomes. In this case, there are 9 favorable outcomes and 36 total possible outcomes. So, the probability is: \( P(E) = \frac{9}{36} \) Now, we simplify the fraction: \( P(E) = \frac{1}{4} \)

Final Answer

The probability of obtaining a total of 4 or less in a single throw of a pair of dice is \(\frac{1}{4}\) or 25%.