• There are 6 strings clustered together.
• One end of each string is at point Y (the top), and the other is at point X (the bottom).
• First, two of the ends at point X are randomly tied together. Then two more are tied together, and then the last two.
• Next, two ends at point Y are randomly tied together. Then, two more are tied together, and then the last two.
Determine the probability that all the strings will be tied together in one large loop.
(In reply to
Solution? by Kenny M)
After the bottom ties are made, label one pair of tied strings A and B; another, C and D; and the last, E and F.
To be successful (one long loop) A can be tied to C, D, E or F, four out of the five loose ends, so the probability of making success possible at this stage is 4/5.
WLOG, say F was chosen. Whichever of the four remaining loose ends is taken in hand next, two of the other three will continue the successful chain, so that's 2/3 probability.
The probability that success will come both times is therefore 4/5 * 2/3 = 8/15.
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Posted by Charlie
on 2022-10-16 08:49:42 |
re: Solution? -- I agree it is
