Independent Events Question: Coin Tossing

In summary, the problem is to calculate the probability of obtaining the same number of tosses for each of 3 performances in a fair coin toss experiment. The formula P(AB)/P(B) = P(A) is likely needed, and the answer is 1/7. The length of the first sequence (number of tosses) can be 1, 2, 3, etc. The probability of repeating the results 2 more times is calculated for each possible length of the first sequence and then all results are summed.
  • #1
3
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Hello all,

I am working on this problem, have searched my textbook, this forum, etc and am still as lost. I suspect I need to (in some form) use the formula P(AB)/P(B) = P(A) as it is the integral formula of this section. Any suggestions or hints are greatly appreciated.

A fair coin is tossed until a head is obtained for the first time. If this experiment is performed 3 times, what is the probability that exactly the same number of tosses will be required for each of the 3 performances?

Note: the answer is 1/7

My work thus far:

I know n-1 tails must be obtained in each performance

Events:
Ai = a head is obtained on the ith trial
Bi = " " tail " "
P(Ai) = 0.5
P(Bi) = 0.5
 
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  • #2
Well, the length of the first sequence may be 1 , 2 , 3 , etc...

Suppose the length of the first sequence is 1 (you got a head at the first toss).
Then, what is the probability of obtaining again the same sequence 2 more times?

And if the length of the first sequence was 2 , what would be the probability of repeating the results 2 more times?

And if the length was 3?

And then, finally, you should sum all this parcels...
 
  • #3
Rogerio said:
Well, the length of the first sequence may be 1 , 2 , 3 , etc...

Suppose the length of the first sequence is 1 (you got a head at the first toss).
Then, what is the probability of obtaining again the same sequence 2 more times?

And if the length of the first sequence was 2 , what would be the probability of repeating the results 2 more times?

And if the length was 3?

And then, finally, you should sum all this parcels...

Thank you, that was very helpful!
 

1. What are independent events?

Independent events are events that do not affect each other's outcome. In other words, the outcome of one event has no influence on the outcome of the other event.

2. How do you calculate the probability of independent events?

The probability of independent events can be calculated by multiplying the probabilities of each event. For example, the probability of getting heads on a coin toss twice in a row would be 1/2 x 1/2 = 1/4.

3. What is the difference between independent and dependent events?

Unlike independent events, dependent events are events that do affect each other's outcome. The outcome of the first event influences the probability of the second event.

4. Can you give an example of independent events?

An example of independent events is rolling a dice and flipping a coin. The outcome of rolling the dice does not affect the outcome of flipping the coin.

5. How can you visually represent independent events?

Independent events can be visually represented using a tree diagram. Each branch represents a different outcome, and the probabilities of each branch can be multiplied to calculate the overall probability of the events.

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