If we spin the spinner once, we can get two possible outcomes (red or blue).
If we spin it twice, the outcomes can be (blue, blue), (blue, red), (red, blue), (red, red); this is, 4 different results.
Then, if we spin the spinner 7 times, there are 2^7=128 possible outcomes.
Finally, we can get any of the 128 possible outcomes from the spinner and rolling a 1; similarly, for rolling a 2, 3,..., 6.
Therefore, the number of possible outcomes of spinning the spinner seven times and rolling a die is
[tex]2^7\cdot6=128\cdot6=768[/tex]There are 768 possible outcomes in the sample space.
