Probability a coin lands on head

In summary, the conversation discusses how to calculate the variance in the number of flips until the kth head appears for a coin with a probability of p for heads on each flip. James is advised to fill out the Homework Help Template form, which includes relevant equations and attempted solutions, in order to receive assistance. The formula for the negative binomial distribution is mentioned as a potential solution.
  • #1
james2000
2
0
For A coin that comes up heads independently with probability p on each flip what is the variance in the number of flips until the kth head appears ?
 
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  • #2


James, nobody is going to work your homework problems for you. Finish filling out the form showing the relevant equations and what you have tried. Then someone will help you.
 
  • #3


what form ?
 
  • #4


in order to get say r heads you need to flip the coin at least r times. thus for x>=r the number of possible ways to get r-1 heads in x-1 trials is (x-1)choose(r-1) without respect to order. on the xth trial we will get the rth success. thus since the trials are independent r of those trials have probability p for heads and x-r the remaining trials are all tails which have probability q = 1-p. we form the product of these total number of success and failures with the number of ways in which they may occur and we arrive at the negative binomial distribution. this distribution has a variance can you look it up and calculate it?
 
  • #5


james2000 said:
what form ?

The Homework Help Template form that you are provided when you start a new thread here in the Homework Help forums. It has sections where you fill in the relevant equations, and where you show us your attempt at a solution.

It's the form you deleted when you started this thread, apparently.
 

Related to Probability a coin lands on head

What is the probability of a coin landing on heads?

The probability of a coin landing on heads is 50%, assuming the coin is fair and has an equal chance of landing on either heads or tails.

How do you calculate the probability of a coin landing on heads?

To calculate the probability of a coin landing on heads, you can use the formula: Number of desired outcomes / Total number of possible outcomes. In this case, there is 1 desired outcome (heads) out of 2 possible outcomes (heads or tails), giving a probability of 1/2 or 50%.

Does the probability of a coin landing on heads change over time?

No, the probability of a coin landing on heads does not change over time. Each flip of a coin is an independent event, meaning the outcome of one flip does not affect the outcome of another. Therefore, the probability remains at 50% for each flip.

What is the relationship between the number of coin flips and the probability of getting heads?

As the number of coin flips increases, the probability of getting heads approaches 50%. For example, if you flip a coin 10 times, you could get heads 5 times or more than 5 times, but on average you would get heads 50% of the time.

How does the weight or size of a coin affect the probability of it landing on heads?

The weight or size of a coin does not affect the probability of it landing on heads. As long as the coin is fair and has an equal chance of landing on either heads or tails, the probability will remain at 50% regardless of its weight or size.

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