Question 116997

Flipping coins
If you want to know the {{{probability}}} of a coin landing {{{heads}}}, heads is the favorable outcome. There is {{{only }}}{{{one}}}{{{ way}}} for a coin to land heads, so the {{{numerator}}} of the{{{ probability}}}{{{ fraction}}}{{{ is }}}{{{1}}}. 
The sample space consists of the total number of ways that a coin can land. Since a coin can {{{only}}} land {{{either}}}{{{ heads}}}or {{{tails}}} – {{{2 ways}}} - the sample space is made up of {{{only }}}{{{two}}}{{{ possible}}}{{{ outcomes}}} and the denominator of the probability fraction is {{{2}}}. 
Thus the probability of a coin landing heads is {{{1/2}}}, which is the same as saying that a coin lands heads {{{50}}}% of the time. 
What is the probability of the coin landing tails? We can do the same analysis as for the coin landing heads, finding a probability of {{{1/2}}}, or, knowing that if a coin doesn't land heads it has to land tails, and understanding that {{{the}}}{{{ sum }}}of the {{{probabilities}}} MUST be equal to {{{1}}}, subtract: 
the probability of a coin landing tails must be {{{1 - 1/2 =1/2}}}. 

In this case, {{{both}}}{{{ probabilities}}} (a 1/2 chance of landing either heads or tails) remain {{{true}}}; NO MATTER HOW MANY TIMES you flip a coin, {{{each}}} time the coin is EQUALLY likely to fall {{{heads}}} or {{{tails}}}. 

Even if your coin has fallen heads {{{50}}} times {{{in}}}{{{ a}}}{{{ row}}}, the chance that the next toss will fall tails is still {{{1/2= 50}}}%. 

So, if you get tails {{{3}}} times in a row your chances of getting heads on your next toss is NOT greater than {{{50}}}%.