# What Would You Do If You Win The Lottery

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The probability of its possible values from impossible to certain.

An example is like asking your father for some money. But as an alternative, instead of giving you money, he decides to have fun with it. He decides to flip a coin. It depend on what the coin lands on if you will receive money or not. If the coin lands on “heads” yo win and he will give you 20 dollars. If you are unlucky and the coin lands on tails, you lose, and will receive nothing.‘In this example, we would say that the payout associated with the event that the coin lands “heads” is $20, and the payout associated with “tails” is $0. ‘) but before saying yes and accepting your father 's offer you go and ask your mother for some extra money. She decides to play a game with you too just like your father.she makes a different offer. She will roll a die, and give you $3 for every spot that turns up. Her offer is , if she rolls a 1, she will give you $3; if she rolls a 2, she will give you $6.00 (= 2 x $3.00), ... if she rolls a 6, she will give you $18 (= 6 x $3.00)). You decided to see witch one is a better offer to take.“ the most common way of evaluating these alternatives is to calculate the

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We can use a variable, such as X to indicate the possible payouts. There are two possible outcomes, “heads” and “tails”. The payout you receive if the coin lands “heads” is $20, and we write: XH = $20. Similarly, if the coin lands “tails” you get nothing,“)

‘In this simple case, the expected value is given by the equation: E(X) = ( pH x XH ) + ( pT x XT ) ⇔ E(X) = ( x 20 ) + ( x 0 ) ⇔ E(X) = ( 10 ) + ( 0 ) ⇔ E(X) = $10.00 . after you evaluate your mother’s offer. You find out that the expected value here is: E(X) = ( p1 x X1 ) + ( p2 x X2 ) + ( p3 x X3 ) + ( p4 x X4 ) + ( p5 x X5 ) + ( p6 x X6 ) ⇔ E(X) = ( x X1 ) + ( x X2 ) + ( x X3 ) + ( x X4 ) + ( x X5 ) + ( x X6 ) ⇔ E(X) = ( x 3 ) + ( x 6 ) + ( x 9 ) + ( x 12 ) + ( x 15 ) + ( x 18 ) ⇔ E(X) = x (3 + 6 + 9 + 12 + 15 + 18 ) ⇔ E(X) = x (63) ⇔ E(X) = $10.50”

Once you are done comparing your parents offers you decide the probability of getting more money will happen if you take your mother 's offer, and not your father