Question

A single coin is flipped four times. A) Use an organizational strategy to construct the sample space for this situation. B) How many different outcomes are possible?

Answer 1

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