Flipping a coin probability

Question

Are Paul and Alan's conclusions about the coin's fairness statistically valid. why and why not

-Paul flips the coin 10 times.

-Paul says the coin is not fair because 7 of the results are tails.  

-Alex flips the coin 100 times. 

-Alex says the coin is not fair because 52 of the results are tails. 

a) Paul's conclusion is valid, but Alex's conclusion is not valid

b) Alex's conclusion is valid, but Paul's conclusion is not valid

c) Both Paul's and Alex's conclusions are valid.

d) Both Paul's and Alex's conclusions are invalid.

Answer 1

Hi Jordan,

Neither conclusion is valid. Both are invalid. Coin flips are independent events--the result of one toss does not impact another toss. Over the long run, the number of tails should approach 50% (ex. 500 tails of 1000), but it's unlikely that they get exactly that amount. A lower number of tosses--like Paul's ten--is less subject to this, so Paul could get 7/10 tails on a fair coin. A higher number of tosses like 100 comes closer to the 50% average, but it is rarely exactly 50. I hope this helps.