What is the probability distribution for tossing a fair coin 4 times?

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Homework Help Overview

The discussion revolves around determining the probability distribution for the number of heads when tossing a fair coin four times. Participants are exploring the various outcomes and their associated probabilities.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the calculation of probabilities for different numbers of heads, questioning the original poster's approach to finding the probability of obtaining four heads specifically. There is an emphasis on understanding the complete probability distribution rather than a single outcome.

Discussion Status

Participants are actively engaging in clarifying the requirements of the problem, noting that a full probability distribution is needed. Suggestions have been made to consider the sample space and count the occurrences of heads for various outcomes.

Contextual Notes

There is a focus on the need to calculate probabilities for multiple outcomes (0 to 4 heads) rather than just a single case. The original poster's misunderstanding of the problem's requirements is evident.

vanitymdl
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Homework Statement


Consider the experiment of tossing a fair coin 4 times. What is the probability distribution of the number X of heads?


The Attempt at a Solution


I got (0.5)(0.5)(0.5)(0.5) = 0.0625 but its wrong and I don't know why
 
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vanitymdl said:

Homework Statement


Consider the experiment of tossing a fair coin 4 times. What is the probability distribution of the number X of heads?

The Attempt at a Solution


I got (0.5)(0.5)(0.5)(0.5) = 0.0625 but its wrong and I don't know why
What you have calculated there is the probability of 4 heads, which is also the probability of zero heads (4 tails).

What is the probability of 3 heads? 2 heads, etc. ?
 
Write out in detail the "sample space" of the experiment (it will have 16 points). Count the number of heads for each of the 16 points. How many points are there in the event {2 heads}? What about for 1 head? For 3 heads?

RGV
 
In other words, the problem asked for the probability distribution, not just the probability of four heads. You also need P(three heads), P(two heads), P(one head), and P(no heads).
 

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