document.write( "Question 116997: This is one question amounst a few more that I have to answer within a essay regarding the Law of Large numbers, is there any way you can help me explain this one please.\r
\n" ); document.write( "\n" ); document.write( "Explain your answer to the following question: Is it true that if I get tails 3 times in a row that my chances of getting heads on my next toss is greater than 50%?
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Algebra.Com's Answer #85075 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "Flipping coins
\n" ); document.write( "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 $\"+probability\"$ $\"+fraction\"$ $\"+is+\"$ $\"1\"$ .
\n" ); document.write( "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 $\"2\"$ .
\n" ); document.write( "Thus the probability of a coin landing heads is $\"1%2F2\"$ , which is the same as saying that a coin lands heads $\"50\"$ % of the time.
\n" ); document.write( "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 $\"1%2F2\"$ , 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:
\n" ); document.write( "the probability of a coin landing tails must be $\"1+-+1%2F2+=1%2F2\"$ . \r
\n" ); document.write( "\n" ); document.write( "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 $\"tails\"$ . \r
\n" ); document.write( "\n" ); document.write( "Even if your coin has fallen heads $\"50\"$ times $\"in\"$ $\"+a\"$ $\"+row\"$ , the chance that the next toss will fall tails is still $\"1%2F2=+50\"$ %. \r
\n" ); document.write( "\n" ); document.write( "So, if you get tails $\"3\"$ times in a row your chances of getting heads on your next toss is NOT greater than $\"50\"$ %.
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