Problema Solution
You are playing a game with a friend in which you toss a fair coin. Your friend pays you a nickel if it's heads, and you pay your friend a nickel if it's tails. You win 10 times in a row and want to stop, but your friend says, "Let's play one more time, double or nothing. I'm due to win." What's the expected value of this game?
$
What is your response to your friend?
Answer provided by our tutors
Then the expected value of the outcome is defined as the sum of the products of the outcomes’ values and their respective probabilities.
1 nickel = 5 cents
you win 10 times means you have worn 10 nickles = 10*5 = 50 cents
E = 50* P(win double) + 0* P(lose all)
E = 50*(1/2) + 0*(1/2)
E = 25 cents
the expected value of the game is 25 cents.