The probability of getting a head is 1/2 and so it is for tail. When you toss a coin once, the probability of not getting a head (which is the same as getting a tail) is 1/2. Now the probability of not getting a head on the second toss too is 1/2. So the probability of getting a head at the third toss should be:
Probability of not getting a head at the first toss * Probability of not getting a head at the second toss * Probability of getting a head at the third toss = (1/2)(1/2)(1/2) = 0.125.
0.125 is less than 0.5, which is the probability of getting a head. Now, thinking intuitively and not mathematically, shouldn't the probability of getting a head (or a tail) keep on increasing as I do more and more tosses? That is, if I do not get a head at the first toss, probability of getting it at the first toss should be greater and so on. Could anyone please clarify what I am thinking wrong?
Best Answer
Let's make it simple: two tosses. The probability of getting an head on the first toss is $0.5$, the probability of getting an head on the second toss is $0.5$. the probability of getting at least one head in two tosses is bigger than $0.5$. You can do it counting the outcomes: HH, HT, TH, TT where H stands for head and T stands for tail. There are $3$ outcomes with an head out of all the $4$ possible outcomes. So the probability of getting at least one head increses and for two tosses is $3/4=0.75$. Now try to generalize this to $3$ and to $n$ tosses if you're interested.