# What will be the probability of getting Heads at 41th toss after first 40 toss were all tales?

So, imagine, I have fixed probsbility of 0.6 for heads and 0.4 for tales

No matter how many times I toss, probsbility will reach that value So I tossed the coin 60 times and miraculously first 60 toss were all tales. This will intact intuitive increase the probability of heads becoming more often.

How do I formulate the probability of next coin toss being head?

• It is "tails" ...and what value do you mean in "...will reach that value"? And with your info, the probability of tossing 60 consecutive tails is aprox $\;1.33\times 10^{-24}\;$ , a number so ridiculously low that it could practically be considered zero. Also, what does "...will intact intuitive increas" mean? – DonAntonio Dec 25 '17 at 8:26
• Suppose if I toss a coin 100 times and first 2 toss were tails, and intuitively I believe probability of heads coming out in next toss is more!! What is that specific probsbility – dark silence Dec 25 '17 at 22:16
• That probability is then whatever you want it to be as your belief in what the outcome can be affects decisively the probabilty of the actual outcome for you ...! – DonAntonio Dec 25 '17 at 22:27
• Okay!! I don’t know if you watch football or not, suppose Brazil won World Cup 3 times in a row!! So probability Brazil winning fourth World Cup is low!! Meaning probability of other country winning the cup after 3 wins is higher – dark silence Dec 26 '17 at 8:53
• I have found the answer myself!! – dark silence Dec 26 '17 at 8:54

There is the mathematical model of a ${\bf p}=(0.6,0.4)$ coin. In this model, after you have observed $40$ tails in a row the probability for tail at the next throw is $0.4$.