This question may seem fundamental, I am confused can someone help me with the below problem
Probability of getting 7 continuous heads, if I understand it right is 1/2 pow 7, which is 0.007813, Can I say probability of not getting heads on 7th time is 0.992188.
But, each time I toss the probability of getting heads is 0.5 as H/T is an independent events.
So the confusion I am having is, when I am tossing for the 7th time after 6 continuous heads, what is the probability of head is it 0.007183 or 0.5
Thanks for the reply. I understand the Coin has no memory(When I said its independent it addresses this) and each trail the chance of occurance of heads is 0.5.
Now Lets say I got 14 continuous heads and 15 th time to get a head is 0.0000305176?, if so doesnt tht mean probability of getting a head for 15th time is very less?(Can I comment as the rare probabilities occur, the coin is baised? )
How do I corelate these 2 scenarios and understand this rare probability(combination of independent events, combinedly looking at the nature of randomness it need to flow) and in that event(15th trail) the chance of 0.05 as getting a head is independent.
These 2 different probabilities in the 15th trail makes things confusing for me
I am here in this forum to learn. I appreciate if you can explain me in detail
The chance you have of getting a head on the next toss depends on whereabouts in the sequence you are.How do I corelate these 2 scenarios and understand this rare probability(combination of independent events, combinedly looking at the nature of randomness it need to flow) and in that event(15th trail) the chance of 0.5 as getting a head is independent.
For example from the first toss the chance of heads is
On the second toss it will be because the first toss is not counted
On the th toss it will be where
Using that formula if we look at the chance of getting 15 heads in a row (n=15):
First toss (k=1):
Second toss (k=2):
Eight toss (k=8):
15th toss (k=15):