Question

you roll a die and flip three coins. the number of possible outcomes in the sample space is

Explanation:

Step1: Determine die outcomes

A die has 6 possible outcomes (1, 2, 3, 4, 5, 6).

Step2: Determine coin flip outcomes

Each coin flip has 2 outcomes (heads, tails). For 3 coins, the number of outcomes is $2^3 = 8$ (by the multiplication principle for independent events).

Step3: Calculate sample space size

The total number of outcomes in the sample space is the product of the number of die outcomes and the number of coin flip outcomes. So, $6\times8 = 48$.

Answer:

48