lv100-pokelove
New member
- Joined
- Jul 7, 2016
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A game is being played: there are twelve boxes into which a ball is thrown. The twelve boxes all are painted according to six different colours – orange, blue, red, yellow, green and violet; each colour owns two boxes, so there are two boxes for each of the six colours. The chance of missing when throwing the ball is 0 : the ball has equal chance, in any given throw, of landing in any of the twelve boxes – there is no bias towards any of the boxes; despite how accurate a contestant's aim may or may not be! (just as a fair die has equal chance of landing on any of its six faces).
Eight of the twelve boxes have had a large white X marked on them; the remaining four have been left unmodified. It is clear to the contestants which boxes have been marked with X: one yellow box; one red box; both of the blue boxes; both of the green boxes; one orange box; and one violet box – making a total of eight marked boxes, out of the twelve. The boxes marked with X score higher than the others, when a ball lands in them.
A contestant is given five tries at the game: she will have five balls to throw at the twelve boxes before her, one after another. NB: every time a ball lands in a certain colour, BOTH of the boxes belonging to that colour will be removed from the game, leaving two less boxes left to throw at with the contestants remaining balls. This means no two balls can land in any same colour, or same box.
So, on the contestant's first throw, she will have all twelve boxes – and all six colours – to throw at; but on her last, her fifth, throw, she will only have four boxes (belonging to only two colours) left to throw at.
What is the probability of her landing all five of her balls, one after another, in boxes marked with X.
Could order/permutations have something to do with it?
Eight of the twelve boxes have had a large white X marked on them; the remaining four have been left unmodified. It is clear to the contestants which boxes have been marked with X: one yellow box; one red box; both of the blue boxes; both of the green boxes; one orange box; and one violet box – making a total of eight marked boxes, out of the twelve. The boxes marked with X score higher than the others, when a ball lands in them.
A contestant is given five tries at the game: she will have five balls to throw at the twelve boxes before her, one after another. NB: every time a ball lands in a certain colour, BOTH of the boxes belonging to that colour will be removed from the game, leaving two less boxes left to throw at with the contestants remaining balls. This means no two balls can land in any same colour, or same box.
So, on the contestant's first throw, she will have all twelve boxes – and all six colours – to throw at; but on her last, her fifth, throw, she will only have four boxes (belonging to only two colours) left to throw at.
What is the probability of her landing all five of her balls, one after another, in boxes marked with X.
Could order/permutations have something to do with it?