Question

pinner has 6 equally sized slices numbered from 1 to 6. some are grey and some are white, as shown below. the slices numbered 3 and 4 are grey. the slices numbered 1, 2, 5, and 6 are white. answer the following questions. write each answer as a fraction. the wheel will be spun and will stop on a slice at random. (a) what is the probability that the wheel stops on a white slice? (b) what is the probability that the wheel stops on a white slice, given that the wheel stops on a number less than 5?

Explanation:

Step1: Calculate total number of slices

The spinner has 6 equally - sized slices. So, the total number of possible outcomes \(n(S)=6\).

Step2: Calculate number of white slices for part (a)

The white - numbered slices are 1, 2, 5, 6. So, the number of white slices \(n(W)=4\).
Using the probability formula \(P(A)=\frac{n(A)}{n(S)}\), for the event of stopping on a white slice, \(P(W)=\frac{4}{6}=\frac{2}{3}\).

Step3: Calculate number of slices with number less than 5 for part (b)

The slices with number less than 5 are 1, 2, 3, 4. So, \(n(L) = 4\).
The slices that are white and have number less than 5 are 1, 2. So, \(n(W\cap L)=2\).
Using the conditional - probability formula \(P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{n(A\cap B)}{n(B)}\), for \(A\) (white slice) and \(B\) (slice with number less than 5), \(P(W|L)=\frac{2}{4}=\frac{1}{2}\).

Answer:

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