Let's analyze the problem step by step.

The dartboard has 10 slices, each numbered from 1 to 10. Some are grey and some are white.

Question (a)

We need to find the probability that the dart lands on number 2.

Since there are 10 equally likely slices, the probability of landing on any specific number is: $\frac{1}{10}$

So, the probability that the dart lands on number 2 is: $\frac{1}{10}$

Question (b)

Now, we need to determine the probability that the dart lands on number 2, given that it lands on a white slice.

1. Identify White Slices: From the image, let's count the white slices.

   • The white slices appear to be numbered: 1, 2, 4, 5, 7 (5 slices total).

2. Conditional Probability Calculation: We are looking for the probability that the dart lands on number 2, given that it lands on a white slice.

   Out of the 5 white slices, only one of them is number 2. Thus, the conditional probability is: $\frac{1}{5}$

Final Answers

• (a) Probability of landing on number 2: $\frac{1}{10}$
• (b) Probability of landing on number 2 given that it lands on a white slice: $\frac{1}{5}$

Would you like a further breakdown of these steps?

Additional Questions

1. How would the probabilities change if the dartboard had only 8 slices instead of 10?
2. What is the probability that the dart lands on a grey slice?
3. How would we calculate the probability of landing on an even-numbered slice?
4. If slice 2 was removed, what would be the probability of landing on slice 5?
5. Can you think of a way to generalize these probability problems to any number of slices?

Tip: In probability, always identify the total possible outcomes first, as this forms the basis of the probability fraction.