Question

(a) how many outcomes are there? outcome(s) (b) how many outcomes involve tails and an odd number? outcome(s) (c) how many outcomes do not involve rolling 2? outcome(s)

Explanation:

Step1: Calculate total number of outcomes (a)

For each coin - toss result (2: heads or tails), there are 6 die - roll results. By the counting principle \(2\times6 = 12\).

Step2: Find outcomes with tails and odd number (b)

Odd numbers on a die: \(1,3,5\). So for tails (1 coin - toss result), there are 3 die - roll results. So \(1\times3=3\).

Step3: Calculate outcomes not involving rolling 2 (c)

Total outcomes \(n = 12\). Outcomes with rolling 2: (heads, 2) and (tails, 2) (\(n_{2}=2\)). So \(12 - 2=10\).

Answer:

(a) \(12\)
(b) \(3\)
(c) \(10\)