Final Answer:
The probability of rolling an even number on a fair number cube can be determined by counting the favorable outcomes (even numbers) and dividing by the total possible outcomes.
(B) (a) 1/2, (b) 1/6
Step-by-step explanation:
The probability of rolling an even number on a fair number cube can be determined by counting the favorable outcomes (even numbers) and dividing by the total possible outcomes. In this case, there are three even numbers (2, 4, and 6) out of a total of six numbers on the cube. Therefore, the probability (P) of rolling an even number (a) is calculated as ( P(a) = 3/6 = 1/2
Next, to find the probability of rolling a factor of 6 (b), we need to identify the factors of 6 among the numbers on the cube. The factors of 6 are 1, 2, 3, and 6. There are two numbers on the cube that are factors of 6 (2 and 6). So, the probability (P) of rolling a factor of 6 (b) is P(b) = 2/6 = 1/3.
Therefore, the correct answer is (B) with the probabilities being (a) ( 1/2 and (b) ( 1/3). This is because the probability of getting an even number is indeed ( 1/2), and the probability of rolling a factor of 6 is ( 1/3), aligning with the provided options.
Therefore, the correct option is (B) (a) 1/2, (b) 1/6