Question

a dartboard has 6 equally sized slices numbered from 1 to 6. some are grey and some are white, as shown below. the slices numbered 1 and 3 are grey. the slices numbered 2, 4, 5, and 6 are white. answer the following questions. write each answer as a fraction. a dart will be tossed and will land on a slice at random. (a) what is the probability that the dart lands on a slice with a number greater than 4? (b) what is the probability that the dart lands on a slice with a number greater than 4, given that the dart lands on a white slice?

Explanation:

Step1: Identify total & favorable slices (a)

Total slices: $6$. Slices >4: 5,6 (2 slices).
Probability: $\frac{\text{Favorable}}{\text{Total}} = \frac{2}{6} = \frac{1}{3}$

Step2: Identify white & favorable white slices (b)

White slices: 2,4,5,6 (4 slices). White slices >4: 5,6 (2 slices).
Conditional probability: $\frac{\text{Favorable white}}{\text{Total white}} = \frac{2}{4} = \frac{1}{2}$

Answer:

(a) $\frac{1}{3}$
(b) $\frac{1}{2}$