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# I was doing the laundry and then it happened

Fri 11 Mar, 2016 03:08 am
The final scoop of washing powder in the box co-incided with the last pour of fabric softener from the bottle.

The washing powder box contains 22 scoops. The fabric softener bottle is 2 litres.

I use exactly 1 scoop of powder and 50 ml of fabric softener in every wash.

What is the probability that the last scoop of washing powder occurs when I am using the final 50 ml of fabric softener from the bottle?
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Type: Question • Score: 2 • Views: 1,225 • Replies: 3
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jespah

1
Fri 11 Mar, 2016 06:11 am
@ascribbler,
No idea but you're on a roll. Might want to invest in that lottery ticket today.
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engineer

1
Fri 11 Mar, 2016 06:14 am
@ascribbler,
1/22 * 50/2000
ascribbler

1
Sat 12 Mar, 2016 02:30 am
@engineer,
Quote:
1/22 * 50/2000

1/22* 1/40 = 1/880 has considerable merit as an answer.

However, consider this

When I use the fabric softener from now on, the number of washes until the end of the bottle will be:

40 80 120 160 200 240 280 320 360 400 440

ie 440 washes from exactly 11 bottles

When I use the laundry powder from now on, the number of washes until the

end of the box will be:

22 44 66 88 110 132 154 176 198 220
242 264 286 308 330 352 374 396 418 440

ie exactly 440 washes from 20 boxes

The probability of it happening again is 1/440.

If I had started from a box with 1 portion already used then 22n +21
would never co-incide with a bottle multiple of 40.

Which is why Jespah and I will share the winnings in the unlikely event that I ever buy a lottery ticket.

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