Did we ever explain the Monty Hall problem with logic?

In short, you have 2/3 chance of selecting a coconut when you first choose a door. Every time you select a coconut with your first choice, the host (when removing one of the other two doors) MUST leave you with the yacht, which means when you change under these conditions (which is 2/3 of the time the best thing to do), then you win the yacht.

It's easy to think it's still 50:50, but that assumes the host RANDOMLY removes a door, in which case 1/3 of the time, there would be nothing to win.

Going back to the original problem, (using 9, 8, 8 and 4 , how do you get to 24), it's easier if you turn the problem on it's head, so to speak. The problem is now 4, 8, 8 and 6 to make 24.

Therefore 4 * 8 / 8 * 6 =24.

The solution is a bit more obvious with those fridge magnets which are in the shape of numbers!

## Comments

Good method Mellifera! Thanks. I'd have been at it days!! Got it in about 10 seconds once you said consider what can't happen.

I'm not a quitter though. There must be a formula to do it the other way, even if it does turn out to be a monster.

I'm not a quitter though.

There must be a formulato do it the other way, even if it does turn out to be a monsterS8dding actuarys! Always with the numbers<nnnnaaaaaa>

wayhay!

for others:

This is the same as the 1 – the probability that no students share birthdays.

First student birthday is on any day - 365/365

2nd can only be on - 364/365 if they are to be different

3rd - 363/365…….

25th - 341/365

1–(364/365 x 363/365…..x 341/365) = 0.569

I have no idea what RPN is

Did we ever explain the Monty Hall problem with logic?

In short, you have 2/3 chance of selecting a coconut when you first choose a door. Every time you select a coconut with your first choice, the host (when removing one of the other two doors) MUST leave you with the yacht, which means when you change under these conditions (which is 2/3 of the time the best thing to do), then you win the yacht.

It's easy to think it's still 50:50, but that assumes the host RANDOMLY removes a door, in which case 1/3 of the time, there would be nothing to win.

I did it another way

25 birthdays, number of ways of combining= 365^25 (365 to the power of 25).

Number of ways of arranging 25 unique birthdays= 365*364* ... * 341

So prob(at least two bdays the same)=1- (365*364* ... *341)/365^25=0.569

So long fellow maths geeks. I must go back to work and study.

Till the next maths thread....

Just testing!

Going back to the original problem, (using 9, 8, 8 and 4 , how do you get to 24), it's easier if you turn the problem on it's head, so to speak. The problem is now 4, 8, 8 and 6 to make 24.

Therefore 4 * 8 / 8 * 6 =24.

The solution is a bit more obvious with those fridge magnets which are in the shape of numbers!