Question

why is there 8 possible outcomes to tossing a coin 4 times?

Answer 1

Also another question about probability how come when you have to find the probability of getting a sum you always subtract the x outcome by 1 for example the probability of getting the sum of 3 when you roll two dice numbered 1-6 , you always have to do 2/36 instead of 3/36 and if the sum was 5 you have to do 4/36 instead of 5/36??...

Answer 2

When you toss a coin 4 times, there are 2 possibilities for the 1st toss, 2 for the second, and so on, so there are 2*2*2*2 = 2^4 = 16 possible outcomes.

Probability is the number of times something happens divided by the
number of times it could happen.

For two dice, here all 36 possibilities:

1 2 3 4 5 6
+-------------------
1 | 2 3 4 5 6 7
2 | 3 4 5 6 7 8
3 | 4 5 6 7 8 9
4 | 5 6 7 8 9 10
5 | 6 7 8 9 10 11
6 | 7 8 9 10 11 12

When tossing two dice and determining the sum, there are 6 possible values for the 1st toss and 6 for the second for a total of 6*6=6^2 = 36. This is the total number of outcomes possible. You see all possibilities in the table above.

For the sum to be 3 we can have a 1 in one toss and 2 on the second - there two ways to get a sum of 3 out of 36 - so probability of a sum of 3 is 2/36.

Similarly, for other sums:

For a 5 , there are 4 ways, see table above - so probability of a sum of 5 is 4/36

Hope this helps.