Absolutely, let's solve each part step-by-step:
### (a) Probability of selecting a grey ball
To determine the probability of selecting a grey ball:
- The grey balls are numbered 1, 2, 5, and 7.
- There are 4 grey balls out of a total of 8 balls.
The probability of selecting a grey ball is:
[tex]\[ \text{Probability (grey)} = \frac{\text{Number of grey balls}}{\text{Total number of balls}} = \frac{4}{8} = \frac{1}{2} \][/tex]
### (b) Probability of selecting a ball with an even number
To determine the probability of selecting a ball with an even number:
- The even-numbered balls are 2, 4, 6, and 8.
- There are 4 even-numbered balls out of a total of 8 balls.
The probability of selecting an even-numbered ball is:
[tex]\[ \text{Probability (even)} = \frac{\text{Number of even-numbered balls}}{\text{Total number of balls}} = \frac{4}{8} = \frac{1}{2} \][/tex]
### (c) Probability of selecting either a white ball or a ball with an odd number
To determine the probability of selecting either a white ball or a ball with an odd number:
- The white balls are numbered 3, 4, 6, and 8.
- The odd-numbered balls are 1, 3, 5, and 7.
- We list out all the white or odd balls without double-counting any balls:
- White balls: 3, 4, 6, 8
- Odd balls: 1, 3, 5, 7
- Combining these lists and removing duplicates, we get: 1, 3, 4, 5, 6, 7, 8 (7 unique balls).
The probability of selecting a white ball or an odd-numbered ball is:
[tex]\[ \text{Probability (white or odd)} = \frac{\text{Number of white or odd balls}}{\text{Total number of balls}} = \frac{7}{8} \][/tex]
### Summary
- The probability of selecting a grey ball is [tex]\(\frac{1}{2}\)[/tex].
- The probability of selecting an even-numbered ball is [tex]\(\frac{1}{2}\)[/tex].
- The probability of selecting either a white ball or a ball with an odd number is [tex]\(\frac{7}{8}\)[/tex].
