Question

1. the following spinner is spun and a normal six - sided die is rolled. the product of their respective result

10b what is the probability that the product was a multiple of 4 given that a 2 was spun?
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Explanation:

Step1: Identify outcomes when 2 is spun

When 2 is spun, the die rolls (3,4,5,6) give products: \(2\times3 = 6\), \(2\times4 = 8\), \(2\times5 = 10\), \(2\times6 = 12\). So there are 4 possible outcomes.

Step2: Identify multiples of 4 among these

Check which products are multiples of 4: \(8\) (multiple of 4), \(12\) (multiple of 4). \(6\) and \(10\) are not. So 2 favorable outcomes.

Step3: Calculate probability

Probability = \(\frac{\text{Number of favorable outcomes}}{\text{Total outcomes when 2 is spun}}=\frac{2}{4}=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)