Gregory J. answered • 04/09/20
Professional Math Tutor/Teacher, 2500+ Hours, 1000+ 5-Star Ratings
Hi Valencia!
To do this kind of problem, we must remember that a sample space for an experiment contains all of the possible outcomes of the experiment. So, say for part (a), what we are looking for is how many outcomes are possible if we flip a coin three times. And for part (b), we're after how many outcomes are possible if we flip a coin eight times. And then for part (c) we derive the general formula.
For part (a), if we flip the coin once, there are only two outcomes: heads and tails. If we flip it again, we have the same two outcomes: heads and tails. Same on the third flip: two outcomes, heads and tails. The total possible outcomes is 2*2*2=8, so the sample space size is 8. Notice the number of flips is the number of 2's that were multiplied. This pattern will show up in part (b): for eight flips, we do 2*2*2*2*2*2*2*2=256, giving us a sample space with size 256. Also, in part (c), we have the same pattern: we would do n 2's multiplied together, which can be abbreviated using exponential notation as 2n. So, to recap, part (a) is 2*2*2=8, part (b) is 2*2*2*2*2*2*2*2=256, and part (c) is the formula 2n.
I hope this helps!
