Question

Suppose x coins are tossed. Write an expression to represent the number of possible outcomes.

Answer 1

We know that one coin has 2 sides, this makes it so the expression is 2 multiplied by x, or 2x

Answer 2

`= 2^x`

Explanation:

One coin tossed:

Total outcomes = {H,T} =2
`= 2^1`

Two coins tossed:

Total outcomes :{HH,HT,TH,TT} = 4
`= 2^2`

Three coins are tossed:

Total outcomes : {HHH,HHT, HTT,TTT,THH,TTH,THT,HTH} =8
`= 2^3`

So, 1 coin tossed
`= 2^1`

2 coins tossed
`= 2^2`

3 coins tossed
`= 2^3`

Continuing in this manner ..

x coins tossed
`= 2^x`

Thus an expression to represent the number of possible outcomes when x coins are tossed :
`2^x`