Here are the chances of taking out one particular number in each round e.g. £250,000


Round 1

(1/22)+(1/21 x 20/21)+(1/20 x 19/20)+(1/19 x 18/19)+(1/18 x 17/18 )

= 24.06 (2dp)

Round 2

(1/17)+(1/16 x 15/16)+(1/15 x 14/15)

= 17.96% (2dp)

Round 3

(1/14)+(1/13 x 12/13)+(1/12 x 11/12)

= 21.88% (2dp)

Round 4

(1/11)+(1/10 x 9/10)+(1/9 x 8/9)

= 27.97% (2dp)

Round 5

(1/8 )+(1/7 x 6/7)+(1/6 x 5/6)

= 39.29% (2dp)

Round 6

(1/5)+(1/4 x 3/4)+(1/3 x 2/3)

= 65%

The reason Round 1's chances are higer than Rounds 2 and 3's are because you open more boxes in Round 1, so there is a greater chance of hitting a big number in that round.

Thanks MisterAl, these are sorted now

Sadly this is wrong, but I'll leave it to you to work out why!

Let us suppose that a player has three boxes (plus their own) and must open three of them, hence leaving there own box.

Naturally, the probabilithy of avoiding one box is 75%, as that's the probability it is in your box; but your method would suggest that it's actually (1/2) + (1/3) + (1/4) = 13/12. Looks like something went wrong.