Expected values probability help

In summary, the expected value for this game is - $3.25. This is calculated by taking the probability of getting 3 tails (3/8) and multiplying it by the winnings of $26, adding the probability of getting 2 tails (3/8) and multiplying it by the winnings of $13, subtracting the probability of getting no tails (4/8) and multiplying it by the loss of $26, and finally adding the probability of getting 1 tail (1/8) multiplied by $0 (since no one wins in this scenario). The mistake in the original equation was in computing the probabilities, as the probability of getting 2 heads in 3 tosses is actually 3/8,
  • #1
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A fair coin is tossed 3 times, and a player wins $26 if 3 tails occur, wins $13 if 2 tails occur, and loses $26 if no tails occur. If 1 tail occurs, no one wins. what is the expected value?


i don't really understand what does the "if 1 tail occurs , no one wins. how do you set up that?

i only set up up to ( $26*3/8) + ($13* 2/8) -(26* 4/8) how do i set up the if 1 tail occurs?
 
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  • #2
mtingt said:
i don't really understand what does the "if 1 tail occurs , no one wins. how do you set up that?

Use $0 for the winnings.

i only set up up to ( $26*3/8) + ($13* 2/8) -(26* 4/8) how do i set up the if 1 tail occurs?[/

Your probabilities add up to more than 1, so they are wrong.
 
  • #3
if i use 0 for the winnings that 1 tail occurs that just means i add 0 to the end of my equation?
($26*3/8) + ($13* 2/8) -(26* 4/8) + 0 (1/8)

isnt that still the same?
so what is wrong with my equation?
 
  • #4
mtingt said:
if i use 0 for the winnings that 1 tail occurs that just means i add 0 to the end of my equation?

($26*3/8) + ($13* 2/8) -(26* 4/8) + 0 (1/8)
isnt that still the same?
Yes. The zero just shows a grader than you know what you are doing.

so what is wrong with my equation?

You have computed the probabilities incorrectly. For example, the probability of getting 2 heads in 3 tosses isn't 2/8. Of the 8 possible results of tossing 3 coins, there are 3 possible ways that one can get 2 heads and 1 tail.
 
  • #5
Stephen Tashi said:
You have computed the probabilities incorrectly. For example, the probability of getting 2 heads in 3 tosses isn't 2/8. Of the 8 possible results of tossing 3 coins, there are 3 possible ways that one can get 2 heads and 1 tail.

oh wow, i can't believe i made such a stupid mistake, thank you for helping me out
 

1. What is an expected value in probability?

The expected value in probability is a measure of the average outcome of a random variable over many trials. It is calculated by multiplying each possible outcome by its probability and summing them together.

2. How is expected value used in real life?

Expected value is used in various real-life situations such as in insurance, finance, and gambling. It helps individuals and businesses make decisions by predicting the average outcome of a certain event.

3. What is the difference between expected value and actual value?

Expected value is a predicted average outcome based on probability, while actual value is the observed outcome from a single trial. Expected value may not always equal to the actual value, but over many trials, it should converge to the expected value.

4. How do you calculate expected value with a probability distribution?

To calculate expected value with a probability distribution, you need to multiply each possible outcome by its probability and sum them together. This can be represented by the formula E(X) = ΣxP(x), where x is the value and P(x) is the probability of that value.

5. Can expected value be negative?

Yes, expected value can be negative. This happens when the possible outcomes have negative values or when the probabilities are negative. However, in real-life applications, negative expected values are often interpreted as unfavorable outcomes.

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