The expected value of a player’s winnings is positive, but we want to make it negative. Which of the following changes to the game would make the expected value negative?Increase the penalty to ₹25Decrease the prize money to ₹90
Question
The expected value of a player’s winnings is positive, but we want to make it negative. Which of the following changes to the game would make the expected value negative?Increase the penalty to ₹25Decrease the prize money to ₹90
Solution
The expected value of a player's winnings is calculated by multiplying the probability of each outcome by the amount won or lost in that outcome. If the expected value is currently positive, it means that on average, the player is winning money.
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Increasing the penalty to ₹25: This would mean that when the player loses, they lose more money. This would decrease the expected value, because the losses are now larger. If the expected value was only slightly positive before, this could make it negative.
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Decreasing the prize money to ₹90: This would mean that when the player wins, they win less money. This would also decrease the expected value, because the winnings are now smaller. Again, if the expected value was only slightly positive before, this could make it negative.
So, both of these changes could potentially make the expected value negative, depending on the probabilities of winning and losing and the amounts won and lost. However, without knowing these probabilities and amounts, it's impossible to say for sure which change would be more effective.
Similar Questions
Suppose you’re playing a game using two dice. Upon throwing the two dice simultaneously, if their sum equals 4, then you get ₹1,000. If their sum is anything other than 4, you lose ₹100. What is the expected earning/loss in this game?Note:1. Round off your final answer to two decimal places. If your answer is 1.333333, write 1.33 in the box.2. If the expectation is a loss, make sure you write a negative number. For instance, −2.5 is a valid answer.
This question is a continuation of the previous question. Based on the expected value of the previous question, which of the following is a possibility for Rahul?Note: Multiple options may be correct.Rahul wins ₹50,000 prize money in the first game.Rahul loses all the first 100 games.Rahul loses ₹500 rupees in the first game.
Suppose we change the game’s rules to the following:Outcome Prize4 red balls +1504 blue balls -150Any other outcome -10What will be the expected value for X (the amount of money won by a player after playing the game once)?-2.5-5+2.5+7.5
Rahul wants to play a poker game. The entry charge for the game is ₹2,000, which is non-refundable, and the probability that Rahul will win a poker game is 3%. The prize money is ₹50,000. If Rahul wins, he gets the prize money. If he loses, he gets nothing. What is his expected earning/loss per game? Note:1. Round off your final answer to two decimal places. If your answer is 1.333333, write 1.33 in the box.2. If the expectation is a loss, make sure you write a negative number. For instance, −2.5 is a valid answer.
Now, can you calculate the expected value of X (where X is the money won by the player after playing the game once)?X (Money won after playing once) Probability+150 0.133−10 0.867You can use this probability distribution to find the answer
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