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Question 6 (5 points)

A fair die is rolled once. What is the probability of rolling a 4 or a 6?

A. [tex]\(\frac{1}{6}\)[/tex]

B. [tex]\(\frac{2}{3}\)[/tex]

C. [tex]\(\frac{1}{3}\)[/tex]

D. [tex]\(\frac{5}{6}\)[/tex]


Sagot :

To determine the probability of rolling a 4 or a 6 on a single roll of a fair six-sided die, we can follow these steps:

1. Understand the Basics of Probability:
- A fair die has 6 faces, each numbered from 1 to 6.
- Each face has an equal probability of landing face up.

2. Determine the Probability of Rolling a Specific Number:
- Since there are 6 faces, the probability of rolling any specific number (such as a 4 or a 6) is [tex]\( \frac{1}{6} \)[/tex].

3. Identify Mutually Exclusive Events:
- Rolling a 4 and rolling a 6 are mutually exclusive events, meaning these events cannot occur simultaneously (you cannot roll both a 4 and a 6 at the same time on a single die).

4. Calculate the Probability of Either Event Occurring:
- Since rolling a 4 and rolling a 6 are mutually exclusive events, we can add their individual probabilities together to find the probability of either event occurring.

- Probability of rolling a 4: [tex]\( \frac{1}{6} \)[/tex]
- Probability of rolling a 6: [tex]\( \frac{1}{6} \)[/tex]
- Combining these probabilities for mutually exclusive events gives:
[tex]\[ P(\text{4 or 6}) = P(\text{4}) + P(\text{6}) = \frac{1}{6} + \frac{1}{6} \][/tex]

5. Perform the Addition:
- Add the probabilities:
[tex]\[ \frac{1}{6} + \frac{1}{6} = \frac{2}{6} \][/tex]

6. Simplify the Fraction:
- Simplify [tex]\( \frac{2}{6} \)[/tex]:
[tex]\[ \frac{2}{6} = \frac{1}{3} \][/tex]

Therefore, the probability of rolling a 4 or a 6 on a single roll of a fair die is [tex]\( \frac{1}{3} \)[/tex].

So, the correct choice is:
c) [tex]\( \frac{1}{3} \)[/tex]
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