Question

six balls numbered from 1 to 6 are placed in a bag. some are grey and some are white, as shown below. the balls numbered 1 and 4 are grey. the balls numbered 2, 3, 5, and 6 are white. answer the following questions. write each answer as a fraction. a ball will be randomly selected. (a) what is the probability that a number greater than 4 is selected? (b) what is the probability that a number greater than 4 is selected, given that the selected ball is white?

Explanation:

Step1: Identify total and favorable balls (a)

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

Step2: Identify white and favorable white balls (b)

White balls: 2,3,5,6 (count=4). White balls >4: 5,6 (count=2).
Conditional probability: $\frac{\text{Favorable white}}{\text{Total white}} = \frac{2}{4} = \frac{1}{2}$

Answer:

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