Let's examine the problem step-by-step.

Information from the Spinner

The spinner is divided into 6 equal slices, numbered 1 to 6. Each slice has an equal chance of landing, and some slices are white while others are grey.

From the image:

• Grey slices: 2, 4, and 6
• White slices: 1, 3, and 5

Questions to Solve

(a) Probability that the wheel stops on a slice with a number less than 5

The numbers less than 5 on the spinner are 1, 2, 3, and 4. That means there are 4 slices that satisfy this condition out of a total of 6 slices.

So, the probability is: $\frac{4}{6} = \frac{2}{3}$

(b) Probability that the wheel stops on a slice with a number less than 5, given that the wheel stops on a grey slice

Since the wheel has stopped on a grey slice, we only consider the grey slices: 2, 4, and 6.

Out of these grey slices, the slices with numbers less than 5 are 2 and 4 (2 out of 3 grey slices).

Thus, the conditional probability is: $\frac{2}{3}$

Answers

• (a) The probability that the wheel stops on a slice with a number less than 5: $\frac{2}{3}$.
• (b) The probability that the wheel stops on a slice with a number less than 5, given that it stops on a grey slice: $\frac{2}{3}$.

Would you like further clarification on any of the steps?

Additional Questions

1. What is the probability that the wheel stops on a white slice?
2. What is the probability that the wheel stops on a grey slice?
3. What is the probability that the wheel stops on a slice with an even number?
4. What is the probability that the wheel stops on a slice with a number greater than 3?
5. If the spinner is spun twice, what is the probability that it lands on a grey slice both times?

Tip

When calculating probabilities, always start by identifying the favorable outcomes and the total number of possible outcomes. This will help simplify your calculations.