An experiment consists of rolling a 6 sided number cube then flipping a coin. How many total out comes are in the sample space, and what outcomes would the event "even number and heads" consist of?
To find the total outcomes in the sample space, we need to consider the possible outcomes for each step of the experiment.
- Rolling a 6-sided number cube: There are 6 possible outcomes (numbers 1 to 6).
- Flipping a coin: There are 2 possible outcomes (heads or tails).
To find the total outcomes in the sample space, we multiply the number of outcomes for each step: 6 x 2 = 12 possible outcomes.
The event "even number and heads" would consist of the outcomes where we roll an even number on the number cube and flip a heads on the coin.
From the 6-sided number cube, the even numbers are 2, 4, and 6. From the coin flip, the outcome we're interested in is heads.
So, the event "even number and heads" consists of the following outcomes: (2, heads), (4, heads), and (6, heads).