Question

If a quarter is tossed five times and comes up tails twice and heads three times, the probability of heads on the next two tosses is ...

Answer 1

The probability of heads on the next two tosses is independent of everything that has happened(all the coin tosses) upto that point in time as consecutive coin tosses are independent of each other.

Considering the coin to be fair, the probabilty that the next two tosses will yield heads given that in the before 5 tosses we have got tails twice and heads three times is given by :

P(heads next two tosses / tails twice and heads three times in previous 5 tosses) = P(heads next two tosses) = (1/2) * (1/2) = 1/4

This is because both the events are independent