Calculating Expected Value for Coin Flipping - Tips and Tricks

In summary, if you flip a coin five times, the expected value of getting three heads or tails is 0.5 * 5 = 2.5.
  • #1
LittleTexan
7
0
Expected Value -- Please Help

Hello,

I have this question that is bugging me to death. Ok here it is:

If a coin was flipped a maxium number times of five. What is the expected value for the number of flips required to get either 3 heads or 3 tails.

I know the probability of head or tails is 0.5 and I am not sure where to go from this.

Thanks
 
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  • #2
Look at the probability of getting 3 heads or 3 tails if you flip the coin once, twice, three times, four times, five times.
 
  • #3
LittleTexan said:
Hello,

I have this question that is bugging me to death. Ok here it is:

If a coin was flipped a maxium number times of five. What is the expected value for the number of flips required to get either 3 heads or 3 tails.

I know the probability of head or tails is 0.5 and I am not sure where to go from this.

Thanks

Okay, I think I can help you with this one, but I'll leave the solving up to you. Think about it your p.d.f. of this function - it's binary, isn't it? In other words, if you define "success" to be getting HEADS on a given flip, then "failure" is not getting HEADS, right? So:

[tex]P("success") = p = \frac{1}{2}[/tex] and [tex]P("failure") = 1 - p = 1 - \frac{1}{2} = \frac{1}{2}[/tex].

Now, since x has a binary pdf, we know that:

[tex]P(X=x) = f(x) = \left(\begin{array}{c}n\\x\end{array}\right)p^x(1-p)^{n-x}[/tex]

It should be pretty straightforward from there... n is obviously the number of trials that you're doing, which I think you said was 5. x is the number of desired outcomes that you're looking for (so in your case, x=3).

Now, if you're looking for expected value of x, then you should know that's just:

[tex]\sum_{all x} x f(x) [/tex]

You can figure that one out...
 

1. What is expected value in the context of coin flipping?

The expected value in coin flipping is a mathematical concept that represents the average outcome of a series of coin flips. It is calculated by multiplying the probability of each possible outcome by its respective payoff and summing these values together.

2. How do I calculate the expected value for coin flipping?

To calculate the expected value for coin flipping, you need to determine the probability of each possible outcome (heads or tails) and its respective payoff. Then, multiply the probability of each outcome by its payoff and sum these values together. The result is the expected value.

3. What is the formula for calculating expected value for coin flipping?

The formula for calculating expected value for coin flipping is: Expected Value = (Probability of Heads x Payoff for Heads) + (Probability of Tails x Payoff for Tails).

4. How can I use expected value to make better decisions in coin flipping?

By calculating the expected value for coin flipping, you can determine the average outcome of a series of coin flips. This can help you make better decisions by informing you of the potential risks and rewards associated with each outcome.

5. Are there any tips and tricks for calculating expected value for coin flipping?

One helpful tip for calculating expected value for coin flipping is to assign numerical values to the outcomes (e.g. heads = 1, tails = 0) to make the calculation easier. Additionally, it is important to remember that the expected value is not a guaranteed outcome, but rather an average of all possible outcomes.

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