Answer:
Ito po tama to
Step-by-step explanation:
Let’s imagine we have an auditorium full of people, each of which has been issued a deck of cards and an efficient autoshuffler.
Everyone, draw one card and look at it. If your card is not a heart, thank you for your help, you are dismissed.
Roughly 1/4th the crowd remains. Everyone still here, replace your card in the autoshuffler. Now, draw a card. Exactly like the first time, there’s a 1/4 chance you drew a heart. If you did not, thanks for your help, you are dismissed.
Chances of drawing two hearts in a row, each time from a full freshly shuffled deck, are 1/4*1/4. If each row had 16 people in it to start with, now most rows have only one; some have 2, some have none, but if you add it all together, it’s pretty close to 1 per row.
Now, everyone who is still in the room, replace your card in the autoshuffler, and then draw your third card. 1/4th of you drew a heart, the rest, well, you know the drill folks. Thanks for coming, you came close!
1/4*1/4*1/4 is 1/64. Now, there’s one of you left in every 4 rows, three out of four rows are empty. For every one of you still here, there are sixty three people who left, more or less.
So, replace your cards in your autoshufflers, and draw one last time. Who here drew a heart?
Roughly one in four of you.
1/4*1/4*1/4*1/4=1/256. We started with a little over a thousand people in the auditorium, and there are four of you left, for every one of you, 255 people are waiting outside.
So the answer to the question is 1/256.
But I think you know what’s coming next, right? Everyone replace and draw one last time. And, on average, one person gets a heart. Now, at the small end of the stick here, that often doesn’t work out, we get two hearts or no hearts, or even three hearts. We could even get all four of you drawing hearts.
The odds of you being the one person out of the entire auditiorium who drew a heart this last time are 1/1024
Guess what the odds of all four of you drawing a heart on this last draw were?
Nope.
It’s 1/256. Four draws from freshly shuffled full decks, all coming up the same suit, are 1/256, we already established that. I didn’t ask what the odds were that you were one of the people left to make that draw (that was 1/256, again that was the point of the exercise) But since you’re curious, the odds of you being one of the 1024 people who came in, drew four hearts in a row, and were then part of a set of four people who all drew a heart, are 1/256*1/256, or 1/65536
