I am practicing problem about binomial probability before the semester starts. The problem is like this:
You flip a coin 10 times. You get 4 heads and 6 tails. What is the probability of getting a head on your next flip.
If I understand this right, I just need to multiply p(4 heads and 6 tails) x probability of getting head on a single trial.
Which is:
10C4 x (1/2)^4 x (1/2)^6 x (1/2).
Is there any way to make sure the probability model I make is correct?
Thank you for your time.
On
If I understand this right, I just need to multiply p(4 heads and 6 tails) x probability of getting head on a single trial.
This is the joint probability of the two events "4 heads and 6 tails in first 10 tosses" AND "heads on 11th toss"
The question is asking for the conditional probability of getting heads given your first 10 tosses were 4 heads and 6 tails. Since your previous tosses have no effect on the outcome of your next toss, the probability of getting heads will be 0.5 (assuming a fair coin).
Assuming your coin is fair, the answer is 50%. It has nothing to do with previous result.
Consider a different question: you flip a coin 11 times, what is the probability you have 5 heads and 6 tails. Here you should use the binomial distribution.