Probability question about dealer's schedule

D

David Spence

Member
A dealer you like always has the same, consecutive two days off each week. She was working today. Unfortunately, you forgot to ask her about her schedule. What is the probability that she will be working tomorrow? (Assume she never calls in sick, takes vacation, etc.)
 
David Spence said:
A dealer you like always has the same, consecutive two days off each week. She was working today. Unfortunately, you forgot to ask her about her schedule. What is the probability that she will be working tomorrow? (Assume she never calls in sick, takes vacation, etc.)
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1 in 3. Six days 2 of which she has off.
 
I would disagree. I find that weekend dealers almost never end their shift on a Sunday (or Saturday/Sunday, if it was a swing shift dealer), so the probability would be higher than 33%.
 
Lonesome Gambler said:
I would disagree. I find that weekend dealers almost never end their shift on a Sunday (or Saturday/Sunday, if it was a swing shift dealer), so the probability would be higher than 33%.
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A valid point, but pretend there are no scheduling biases such as this. One hint: it is significant that the dealer's days off are consecutive.
 
Richard Munchkin said:
4 out of 5 that she will be working tomorrow.
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6 days in which the 2 in a row off may occur.
1) Next 2 off.
2) Work tomorrow next 2 off.
3) Next 2 days on. Then 2 off.
4) Next 3 days on. Then 2 off.
5) Next 4 days on. Then 2 days off.

Damn laid it out to show I was right but I must have messed it up in my head calculation. I had 1 in 5 the first time in my head and thought through it again before I submitted my post and got 1 in 4. I should have done it a third time to confirm which was wrong.
 
David Spence said:
A dealer you like always has the same, consecutive two days off each week. She was working today. Unfortunately, you forgot to ask her about her schedule. What is the probability that she will be working tomorrow? (Assume she never calls in sick, takes vacation, etc.)
Click to expand...

NO chance-------------------------------------she's with me tomorrow.:laugh:
 
What day is it today? And what day is treated as the last day of the working week?

If today is the penultimate day of the week, then she must be working tomorrow.
 
Richard Munchkin said:
4 out of 5 that she will be working tomorrow.
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Correct! And, as it turned out, today was part of that 80% :-)

Solution:
Say you see her working on a Friday. The possibilities for her two consecutive days off are:
MT, TW, WTh, SaSu, SuM

We want to know the probability that she'll be working the next day, Saturday. Of her five possible schedules, only one has her off on Saturday. The other four out of five schedules have her working Saturday, so the answer is 4 out 5.
 
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my explanation

The following explanation works. I came up with the same answer with this logic. "today" would be 1 of the 5 days the working days. Only if "today" is the last day of the working week, dealer would be off "tomorrow". That chance would be 1 out of 5.

David Spence said:
Correct! And, as it turned out, today was part of that 80% :-)

Solution:
Say you see her working on a Friday. The possibilities for her two consecutive days off are:
MT, TW, WTh, SaSu, SuM

We want to know the probability that she'll be working the next day, Saturday. Of her five possible schedules, only one has her off on Saturday. The other four out of five schedules have her working Saturday, so the answer is 4 out 5.
Click to expand...
 
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