I mentioned to a colleague that I’d bought two lottery tickets for last weeks Euromillions draw instead of my usual 1 to double my chance at winning. He said “Yeah, that’s not how it works.” I’m sure he is right – but why?
In: 7847
I think your colleague was misunderstanding the math lesson he was trying to apply.
This is the math problem as you understood it, but simplified: take a 6-sided die. You know that, if you roll it, one of the six numbers will show up. You just have to bet on the right number to win the jackpot. So you bet on 1, but then you go “wait, if I do a second bet then I’m more likely to win!” so you bet on 2 as well. You’re only rolling the dice once, but now if the dice lands on 1 OR 2 you win. That actually is doubling your odds.
But this is the math problem as your colleague understood it, but simplified: take a 6-sided die. You know that, if you roll it, one of the six numbers will show up. So you bet on 1, roll it, and it lands on some number other than 1 and you lose. So you go “I’ll bet on 1 again, that doubles my odds of winning!” In this case your odds do not double, because each roll of the dice is a unique event. Dice don’t go ‘oh, I rolled 2 last time, I need to roll 1, 3, 4, 5, or 6 now!’ Each time you roll, the probability is calculated separately. (someone in another comment already did the math to show your actual odds in this kind of situation, so I won’t show that math here.)
TL;DR you’re actually right because you bought two tickets to the same lottery drawing. Your friend would be right if you bought a ticket this week and then a ticket next week and said ‘my odds are doubled!’
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