Let's analyze and solve the probability questions based on the dartboard shown in the image.

Given Information:

The dartboard is divided into 10 equally sized slices numbered from 1 to 10. Some slices are grey, and others are white.

Observations from the Image:

• White Slices: 2, 4, 6, 8, 10 (5 slices)
• Grey Slices: 1, 3, 5, 7, 9 (5 slices)

Questions:

(a) Probability that the dart lands on a white slice.

To calculate this probability, we need the ratio of white slices to the total number of slices.

$P(\text{white slice}) = \frac{\text{Number of white slices}}{\text{Total number of slices}} = \frac{5}{10} = \frac{1}{2}$

Answer for (a): $\frac{1}{2}$

(b) Probability that the dart lands on a white slice, given that it lands on a number less than 9.

1. Numbers less than 9: 1, 2, 3, 4, 5, 6, 7, 8 (8 slices in total).
2. White slices among numbers less than 9: 2, 4, 6, 8 (4 slices).

The probability is the ratio of white slices among those numbered less than 9 to the total number of slices numbered less than 9.

$P(\text{white slice | number < 9}) = \frac{\text{Number of white slices with numbers less than 9}}{\text{Total slices with numbers less than 9}} = \frac{4}{8} = \frac{1}{2}$

Answer for (b): $\frac{1}{2}$

Would you like further details on any part of this solution, or do you have other questions?

Related Questions:

1. What is the probability that the dart lands on a grey slice?
2. If the dart lands on an even-numbered slice, what is the probability that it is white?
3. What is the probability that the dart lands on an odd-numbered slice?
4. Given that the dart lands on a grey slice, what is the probability that it is numbered 5 or higher?
5. If the dartboard had 12 slices instead, what would be the probability of landing on a white slice if 6 slices were white?

Tip:

When calculating conditional probabilities, always focus on narrowing the "sample space" to only the relevant conditions. This reduces errors in calculating the desired probability.