Answer :
Sure, let’s go through each part of the question step-by-step:
### Part (a): Probability that the dice lands on an odd number
A standard six-sided die (often called a fair die) has the numbers 1, 2, 3, 4, 5, and 6 on its faces. We need to determine the probability that when the die is rolled, it lands on an odd number.
1. List the odd numbers on the die: The odd numbers on a six-sided die are 1, 3, and 5.
2. Count the odd numbers: There are 3 odd numbers.
3. Total possible outcomes: Since the die has 6 faces, there are 6 possible outcomes when the die is rolled.
The probability of landing on an odd number is given by the ratio of the number of favorable outcomes (odd numbers) to the total number of possible outcomes (all numbers on the die).
[tex]\[ \text{Probability of odd number} = \frac{\text{Number of odd numbers}}{\text{Total number of outcomes}} = \frac{3}{6} = 0.5 \][/tex]
So, the probability that the dice lands on an odd number is 0.5.
### Part (b): Probability that the dice lands on a number less than 3
For this part, we are considering the numbers on the die that are less than 3.
1. List the numbers less than 3: On a standard die, the numbers less than 3 are 1 and 2.
2. Count the numbers less than 3: There are 2 numbers that are less than 3.
3. Total possible outcomes: There are still 6 possible outcomes when the die is rolled.
The probability of landing on a number less than 3 is given by the ratio of the number of favorable outcomes (numbers less than 3) to the total number of possible outcomes.
[tex]\[ \text{Probability of number less than 3} = \frac{\text{Number of numbers less than 3}}{\text{Total number of outcomes}} = \frac{2}{6} = \frac{1}{3} \approx 0.333 \][/tex]
So, the probability that the dice lands on a number less than 3 is approximately 0.333.
### Summary of Results
- The probability that the dice lands on an odd number is 0.5.
- The probability that the dice lands on a number less than 3 is approximately 0.333.
### Part (a): Probability that the dice lands on an odd number
A standard six-sided die (often called a fair die) has the numbers 1, 2, 3, 4, 5, and 6 on its faces. We need to determine the probability that when the die is rolled, it lands on an odd number.
1. List the odd numbers on the die: The odd numbers on a six-sided die are 1, 3, and 5.
2. Count the odd numbers: There are 3 odd numbers.
3. Total possible outcomes: Since the die has 6 faces, there are 6 possible outcomes when the die is rolled.
The probability of landing on an odd number is given by the ratio of the number of favorable outcomes (odd numbers) to the total number of possible outcomes (all numbers on the die).
[tex]\[ \text{Probability of odd number} = \frac{\text{Number of odd numbers}}{\text{Total number of outcomes}} = \frac{3}{6} = 0.5 \][/tex]
So, the probability that the dice lands on an odd number is 0.5.
### Part (b): Probability that the dice lands on a number less than 3
For this part, we are considering the numbers on the die that are less than 3.
1. List the numbers less than 3: On a standard die, the numbers less than 3 are 1 and 2.
2. Count the numbers less than 3: There are 2 numbers that are less than 3.
3. Total possible outcomes: There are still 6 possible outcomes when the die is rolled.
The probability of landing on a number less than 3 is given by the ratio of the number of favorable outcomes (numbers less than 3) to the total number of possible outcomes.
[tex]\[ \text{Probability of number less than 3} = \frac{\text{Number of numbers less than 3}}{\text{Total number of outcomes}} = \frac{2}{6} = \frac{1}{3} \approx 0.333 \][/tex]
So, the probability that the dice lands on a number less than 3 is approximately 0.333.
### Summary of Results
- The probability that the dice lands on an odd number is 0.5.
- The probability that the dice lands on a number less than 3 is approximately 0.333.
