What is the percentage probability of getting two heads
in a
row in fair coin tosses? Of getting five heads in a row? how would you
experimentally test your prediction about getting five heads in a row?
Answer:
To make it clearer and less ambiguous, the question should really be worded
slightly differently, as
follows:
In fair coin tosses,
what is the probability of getting two heads when tossing two coins?
And what is the probability of getting five heads when tossing five coins?
(this is what the book's author really meant).
The answer is:
The probability of getting head with one unbiased (``fair") coin is = 1/2 =
50%.
Since the coins are independent, the probabilities multiply;
the probability of getting two heads with two coins = the square of the
probability of getting head with one coin =
The probability of getting five heads when tossing five coins
To verify this prediction experimentally, you would have to perform many tosses
of five coins - at least one hundred. For 100 tosses of five coins, you should
observe about three all-heads outcomes. But of course there would be a certain
(small) probability that you would get none or six or more!