The next step, we add the fractions and get this result. To get a common denominator, we can change -3/ 1 to -30/ 10. We need to clean up this expression by multiplying the terms. Now, we have to multiply our columns (expected values times their respective probabilities). So, this will be entered within the last column. The player has to pay $3 to begin the game. This information will now be placed within a table of expected values. The probability of grabbing a red marble is 3/ 10. The probability of grabbing a yellow marble is 1/ 10. The probability of grabbing a blue marble is 2/ 10. The probability of grabbing a green marble is 4/ 10. Placing them in another chart will be the easiest way to organize our information. To construct a table of expected values, we need to know the probabilities of pulling various marbles. The payout depends on what color marble the player pulls, according to this chart. Pay $3 and pull a marble randomly from the bag. Here is a game that involves a marble bag. For the following examples, less steps will be shown. This example had a long explanation because it was necessary to explain all the details of the process. If a player plays 100 games, the player would likely lose 100( 1/ 4), or $25, on average. However, over the long haul, a player will lose a quarter per game. Sure, a player can land on yellow many times in a row. This means a player will lose 1/ 4 of a dollar (or 25 cents), on average, every time the game is played. Since they are all in eighths, add the numerators. So that we can easily combine this expression, transform the -2 into eighths. Here is the resulting calculation:Ĭleaning up the expression gives us this. Once we gain these products, we add them together. Now that we have our table of values, we are going to multiply values times their respective probabilities, like so. This will be the last entry into the table, like so. There is a 100% probability (remember, 100% = 1) of losing this $2. It is incomplete because we have yet to account for one crucial piece of information: the wager. We will fill in the rest of the information into the expected values table. Finally, the chance to land on red is 1/ 8 because red occupies only 1 space out of 8 total spaces. Since blue has 3 spaces, the chance to land on blue is 3/ 8. The probability of landing on yellow is the same, 2/ 8, because there are two yellow spaces. Keep in mind, the expected value (amount the player wins) for purple is $0.50. Let’s fill in the table with the information for purple. So, the probability of landing on purple is 2/ 8. If all the spaces on the spinner are the same size, which is a safe assumption based upon the spinner presented here, there is a 1 in 8 chance of landing on any one space. This requires us to know a little bit about probability, too. To determine who this game favors, we must fill an expected values table. If the spinner lands on red, the player wins nothing. If the spinner lands on blue, the player wins $1. If the spinner lands on yellow, the player wins $5. If the spinner lands on purple, the player wins $0.50. The player pays $2 and spins the spinner.
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