An experiment consists of rolling a 6-sided number cube then flipping a coin. How many total outcomes are in the sample space, and what outcomes would the event “even number and heads” consist of?
For the rolling of the 6-sided number cube, there are 6 possible outcomes (1, 2, 3, 4, 5, or 6).
For flipping the coin, there are 2 possible outcomes (heads or tails).
To determine the total number of outcomes in the sample space, we multiply the number of outcomes for each stage. Thus, the total number of outcomes in the sample space is 6 x 2 = <<6*2=12>>12.
The event "even number and heads" would consist of the outcomes (2, heads) and (4, heads). Note that the coin flip outcome needs to be heads, and the number cube outcome needs to be even.