Answer:
P=0.125
If it is repeated 10,000, it is expected "3 tails in a row" about 1,250 times.
Step-by-step explanation:
When flipping a coin a number of times, we can modeled this as a random variable with a binomial distribution.
In this case, we have to calculate the probability of 3 consecutive tails. If we define p as the probability of getting a tail (which has a value of p=0.5 if it is an unbiased coin), the probability of getting 3 tails in a row is:
[tex]P=p^3=0.5^3=0.125[/tex]
If that event of "flipping a coin 3 times" is repeated 10,000 times, we can expect to have 3 tails in a row about 1,250 times:
[tex]E=nP=10,000*0.125=1,250[/tex]
because we expect 0.125 events of this type for every try, so we can multiply this probability (or expected frequency) by the number of trials and we get the expected number of events described.
