# Expected values probability help

• mtingt
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, #### mtingt 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?

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. 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? 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.

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.