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Chapter 2: Problem 100

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

Short Answer

Expert verified
The probability of obtaining a total of 4 or less in a single throw of a pair of dice is \(\frac{1}{6}\).

Step by step solution

01

Determine the Total Possible Outcomes

When rolling two dice, there are 6 sides on each die, so there are 6 x 6 = 36 possible combinations of outcomes for the two dice.
02

Determine the Favorable Outcomes

To find the favorable outcomes, we need to determine all possible combinations of rolls that result in a sum of 4 or less. Let's list these in a table: Die 1 | Die 2 | Sum ------|-----|---- 1 | 1 | 2 1 | 2 | 3 1 | 3 | 4 2 | 1 | 3 2 | 2 | 4 3 | 1 | 4 As we can see, there are 6 such combinations.
03

Calculate Probability

Now, we can use the formula for probability to calculate the answer: \[P(\text{sum} \le 4) = \frac{\text{Favorable Outcomes}}{\text{Total Possible Outcomes}}\] Plugging in the numbers we found earlier, we get: \[P(\text{sum} \le 4) = \frac{6}{36}\] Simplify the fraction to get: \[P(\text{sum} \le 4) = \frac{1}{6}\] Thus, the probability of obtaining a total of 4 or less in a single throw of a pair of dice is \(\frac{1}{6}\).

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