Question

Determine the number of possible outcomes when tossing one coin ,two coins ,and three coins then determine the number of possible outcomes for tossing N coins

Answer 1

Number of possible outcome for tossing N coins = $2^N$

Solution:

Possible outcomes when tossing one coin = {H, T}

Number of possible outcomes when tossing one coin = 2 $=2^1$

Possible outcomes when tossing two coins = {HH, HT, TH, TT}

Number of possible outcomes when tossing two coins = 4 $=2^2$

Possible outcomes when tossing three coins

                                 = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}

Number of possible outcomes when tossing three coins = 8 $=2^3$

Therefore, the sequence obtained is $2^1, 2^2, 2^3$.

If continue this sequence, we can obtain number of possible outcome for tossing N coins is $2^N$.