How to solve a geometric distribution problem with a biased coin?

In summary, the conversation is about a problem involving a biased coin and determining the probability of obtaining a certain number of heads in a specific number of tosses. The person asking for help initially struggled with understanding the problem but eventually came to a solution with the help of others. The person offering assistance emphasizes the importance of putting in effort and showing work before seeking help on the forum.
  • #1
sasuke0159
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A boy is playing with a biased coin. The probabilty of obtaining a head with the coin is 0.4. Determine the probability that the boy will require at least eleven tosses before obtaining his third head.

I have been trying but can't get it at all... Can someone please explain me how to solve this problem?
 
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  • #2
Ignore the probability for the moment. If the third head occurs after at least eleven tosses what is the maximum number of heads that can have occurred in ten tosses?
 
  • #3
Well i guess the MAX is 2 and min must be zero!
If you come to any conclusion, feel free to explain i'll be around.
 
  • #4
sasuke0159 said:
Well i guess the MAX is 2

Partition the event "A max of 2 heads in 10 tosses" into 3 mutually exclusive events and find their probabilities.
 
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  • #5
sasuke0159 said:
Well i guess the MAX is 2 and min must be zero!
If you come to any conclusion, feel free to explain i'll be around.

What does this mean? PF rules forbid us from solving your problem for you. In fact, you are supposed to show your work first before getting any help.
 
  • #6
No worries, i finally got a hang of this problem. Thanks for all your help.
Well PF actually forbade you guys to solve the problem because it was in the wrong section,i'm new to the forum and am still getting used to it.
By the way about showing my work, what if i didn't really understand the problem and needed someone to help me understand it, PF would not allow it?
 
  • #7
PF rules require you to do some legwork before you can get help here. Chances are you already have, but you need to tell us what you've been thinking. It's not okay to simply say "I don't get it." That's really kind of lazy. What is it specifically that's confusing you? For example, do you not understand the problem statement? Or do you think a certain distribution applies but you don't know how to determine some parameter you need? You need to formulate a specific question.

If you're really at a point where you can't do the above, PF isn't the place for you yet. You shouldn't even be attempting the problem because you don't know the basic material. PF isn't here so students can avoid reading their book, etc.

https://www.physicsforums.com/showthread.php?t=686783
 

1. What is the Geometric Distribution?

The Geometric Distribution is a probability distribution that models the number of trials needed to achieve a success in a sequence of independent and identical Bernoulli trials, where the probability of success remains constant.

2. How is the Geometric Distribution different from the Binomial Distribution?

The Geometric Distribution models the number of trials needed to achieve a success, while the Binomial Distribution models the number of successes in a fixed number of trials.

3. What is the formula for the Geometric Distribution?

The formula for the Geometric Distribution is P(X=k) = p(1-p)^k-1, where p is the probability of success and k is the number of trials.

4. What is the expected value and variance of the Geometric Distribution?

The expected value of the Geometric Distribution is E(X) = 1/p, and the variance is Var(X) = (1-p)/p^2.

5. In what real-life situations can the Geometric Distribution be applied?

The Geometric Distribution can be applied in situations such as modeling the number of attempts needed to win a game, the number of phone calls needed to make a sale, or the number of trials needed to find a defective product in a batch.

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