LR Question 21 Explanation
QUESTION TEXT: Sandy: I play the Bigbucks lottery-that’s the one…
QUESTION TYPE: Flawed Reasoning
DESCRIPTION OF THE GAME: Five numbers are drawn. If you pick the five numbers, you’ll win the pot. There is not a winner every week: someone only wins if their numbers are picked.
ARGUMENTS: Sandy says it’s best to play after there has been no winner for a bit. There’s more money to be won.
Alex thinks that it will be harder to win because there are more players.
ANALYSIS: Alex is wrong. How likely you are to pick the winning five numbers is not affected by the number of players.
Alex said you’re less likely to win with more players. That’s incorrect. You have a 1-in-100,000 chance of winning each week, no matter how many people play (you don’t need to calculate these odds of to answer the question, of course.) Multiple people can pick the winning number. That doesn’t reduce your odds.
Even if you were the only one playing you would still lose for 99,999 weeks for every week you won.
If you had to pick a number between one and ten and you win 2$ if you guess right, your odds of winning aren’t affected by how many people play.
___________
- Sandy didn’t say that. Sandy just said it’s smart to wait for a bigger pot.
- CORRECT. Alex is mistaken: the odds of picking five numbers correctly never change.
- Sandy didn’t say anything about the odds of winning. He just talked about how big the pot would be if you did win.
- If Alex had said this, he would have been correct. The odds of winning in any given week are unaffected by whether anyone won the previous week.
- Show me where Sandy talked about the odds of winning. He only talked about how big the prize would be.
More Resources for Flaw Questions
- Flaw drills: Use these to practice making examples of abstract flaws.
- Intro Course lesson: This intro course lesson covers Flaw questions.
- Mastery Seminar lesson: This LR Mastery seminar lesson covers flaw questions.
You use “he” to describe Sandy and Alex, which made me realize that both of the names are gender neutral in this question. (I was picturing both Alex and Sandy as women.) Funny how internal bias works, lol!
The stimulus says that all players who have picked the five numbers drawn share the money pot, doesn’t that mean that Alex is correct since the smaller the number of winners, the money each person gets?
No, you’re thinking about how much money you win. But “winning the lottery” strictly speaking means getting all the numbers right and winning the biggest prize on offer.
Your odds are based on numbers not prize size. So, like if we have two people
One week: $100 million jackpot —> winner wins the lottery
Next week: tiny $100,000 depleted prize —> winner still wins the lottery
Obviously more *money* for the first lottery winner but they are both lottery winners.