Question

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:

Part (a)

Step1: Identify total and favorable outcomes

Total balls: 6 (numbers 1,2,3,4,5,6). Numbers >4: 5,6 (2 outcomes).

Step2: Calculate probability

Probability = $\frac{\text{Favorable}}{\text{Total}}$ = $\frac{2}{6}$ = $\frac{1}{3}$.

Step1: Identify white balls and favorable among them

White balls: 2,3,5,6 (4 balls). White balls >4: 5,6 (2 balls).

Step2: Calculate conditional probability

Conditional Probability = $\frac{\text{Favorable in white}}{\text{Total white}}$ = $\frac{2}{4}$ = $\frac{1}{2}$.

Answer:

$\frac{1}{3}$

Part (b)