Final Answer:
(a) The probability of selecting a number greater than 4 is 1/3.
(b) Given that the selected ball is grey, the probability of choosing a number greater than 4 is 1/2.
Step-by-step explanation:
In a bag containing six balls numbered from 1 to 6, the balls that qualify as numbers greater than 4 are 5 and 6. As there are two balls out of six that satisfy this condition, the probability of selecting a number greater than 4 can be calculated as the ratio of favorable outcomes (numbers 5 and 6) to the total possible outcomes, resulting in 1/3.
Considering that the selected ball is grey, the initial information becomes crucial. If some of the balls in the bag are grey, then the subset of grey balls should be inspected. In this case, if the selection is restricted to grey balls, the probability changes. There are three grey balls in total, out of which one is greater than 4 (which is a grey number 5). Therefore, within the subset of grey balls, the probability of selecting a number greater than 4 is 1/2, as there is one favorable outcome (grey number 5) out of the two possible grey balls.
Thus, while the overall probability of selecting a number greater than 4 from the entire set of balls is 1/3, the probability of selecting a number greater than 4, given that the chosen ball is grey, becomes 1/2.