Question

You toss a penny and observe whether it lands heads up or tails up. Suppose the penny is fair, i.e., the probability of heads is 1/2 and the probability of tails is y. This means every occurrence of a head must be balanced by a tail in one of the next two or three tosses. if I flip the coin many, many times, the proportion of heads will be approximately %, and this proportion will tend to get closer and closer to 1/2 as the number of tosses increases regardless of the number of flips, half will be heads and half tails. all of the above

Answer 1

It is given that the penny is fair, that is, the probability of heads is 1/2 and the probability of tails is 1/2. This means that for a large number of trials, it is expected to attain tails in 50% of them and heads in 50% of them. Hence, an equal number of heads and tails will be observed if the coin is flipped many times. Therefore, as the trials are increased, the proportion of heads (and tails) will approximate to 1/2 or 50%. Thus, the second option is the correct choice.