Certainly! Let's address each part of the question step-by-step.
### a. The probability of getting the number 4:
When a fair die is tossed, it has 6 faces numbered from 1 to 6. The probability of getting any specific number, such as 4, is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
- Total possible outcomes: 6 (faces of the die)
- Favorable outcomes for getting 4: 1 (only one face has the number 4)
Thus, the probability is:
[tex]\[ \text{Probability} = \frac{1}{6} \][/tex]
[tex]\[ \text{Probability} = 0.16666666666666666 \][/tex]
### b. The probability of getting an even number:
The even numbers on a die are 2, 4, and 6. There are 3 favorable outcomes.
- Total possible outcomes: 6
- Favorable outcomes for getting an even number: 3
Thus, the probability is:
[tex]\[ \text{Probability} = \frac{3}{6} \][/tex]
[tex]\[ \text{Probability} = 0.5 \][/tex]
### c. The probability of getting the number 7:
A standard die only has numbers from 1 to 6. It does not have the number 7. Therefore, the number of favorable outcomes is 0.
- Total possible outcomes: 6
- Favorable outcomes for getting 7: 0
Thus, the probability is:
[tex]\[ \text{Probability} = \frac{0}{6} \][/tex]
[tex]\[ \text{Probability} = 0.0 \][/tex]
### d. The probability of getting either 1, 2, 3, 4, 5, or 6:
These numbers cover all the possible outcomes when a die is tossed. Thus, all faces are favorable.
- Total possible outcomes: 6
- Favorable outcomes: 6
Thus, the probability is:
[tex]\[ \text{Probability} = \frac{6}{6} \][/tex]
[tex]\[ \text{Probability} = 1.0 \][/tex]
### e. The probability of getting a number different from 5:
We are looking for the probability of getting any number except 5. The favorable outcomes in this case are 1, 2, 3, 4, and 6.
- Total possible outcomes: 6
- Favorable outcomes for getting a number different from 5: 5
Thus, the probability is:
[tex]\[ \text{Probability} = \frac{5}{6} \][/tex]
[tex]\[ \text{Probability} = 0.8333333333333334 \][/tex]
I hope this detailed explanation clarifies how we arrive at each of the probabilities for the given scenarios when tossing a fair die!
