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Chapter 2: Problem 93

In a single throw of a single die, find the probability of obtaining either a 2 or a 5 .

Short Answer

Expert verified
The probability of obtaining either a 2 or a 5 in a single throw of a single die is \(\frac{1}{3}\) or approximately 33.33%.

Step by step solution

01

Determine the number of favorable outcomes and total possible outcomes.

There are 6 unique sides to a die, numbered from 1 to 6. The favorable outcomes are obtaining a 2 or a 5. There are 2 favorable outcomes (2 and 5) and 6 total possible outcomes.
02

Calculate the probability of the event happening.

Now that we know that there are 2 favorable outcomes and 6 total possible outcomes, we can find the probability of obtaining either a 2 or a 5 in a single throw of the die. Probability is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case: Probability = \(\frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}\)
03

Substitute the values and compute the probability.

Now, we can plug in the values of the number of favorable outcomes (2) and the total number of possible outcomes (6) to find the probability: Probability = \(\frac{2}{6}\)
04

Simplify the fraction.

The fraction \(\frac{2}{6}\) can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2: Probability = \(\frac{2}{6}\) = \(\frac{2 \div 2}{6 \div 2}\) = \(\frac{1}{3}\)
05

Express the probability as a decimal or percentage (if required).

The probability can also be expressed as a decimal or a percentage. To convert the fraction \(\frac{1}{3}\) to a decimal, divide the numerator by the denominator: Decimal probability = \(\frac{1}{3}\) = 0.333... Percentage probability = 0.333... 脳 100% 鈮� 33.33% The probability of obtaining either a 2 or a 5 in a single throw of a single die is approximately 33.33%.

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