Step-by-step explanation:
- A single coin is known to have 2 sides (The head H and the tail T).
The total number of sample space for n number of coins is expressed as 2ⁿ where
n is the total number of coins flipped.
If a single coin is flipped four times, the total outcome will be expressed as;
2⁴ = 16
Hence there are 16 different possible outcomes.
- To construct the sample space (the 16 possible outcomes)
For one flipped coin, the sample space is represented by the set S₁
S₁ = {H, T}
H is Head
T is Tail
For two flipped coin, the sample space is represented by the set S₂
S₂ = S₁×S₁
S₂ = {H, T}×{H,T}
S₂ ={HH, HT, TH, TT}
For three flipped coin, the sample space is represented by the set S₃
S₃ = S₂×S₁
S₃ = {HH, HT, TH, TT}×{H,T}
S₃ = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
For four flipped coin, the sample space is represented by the set S₄
S₄ = S₃×S₁
S₄ = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}×{H,T}
S₄ ={HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}
Hence the sample space for a single coin flipped 4times is given by the set;
S₄ ={HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT} where;
n(S₄) = 16
