Who can explain this probability problem?

[Pegasus]

I'm struggling to figure out where I am going wrong with this probability problem:

 

You and your sister each baked 12 times in the last 30 days. You picked the 12 days randomly, but you never baked more than once each day. So did your sister. What is the probability that both of you baked on the same day?

 

You can laugh at my approach, which follows; I won't mind.

 

Odds you baked on a particular day:  12/30 or 40%

Odds your sister baked on a particular day: 12/30 or 40%

Odds you both baked on a particular day: 40% x 40% = 16%

Odds that you both baked on the same day during the 30 days: 16% x 12 = 192%

 

 

 

 

[Twolittleboys]

My probability is quite rusty but I think the last step is wrong. I THINK you have to use the negative result (i.e. how likely is it that you did NOT bake both on any of the days) to get to the answer but I may be wrong. 

[eternalsummer]

Likelihood you will have a girl with this pregnancy: 50%

Likelihood you will have a boy: 50%

 

Likelihood you will have at least one girl if you have 2 children: 50% x 2 = 100%  

 

:)

 

--------------------------------------

 

 

Likelihood you will not have a girl this pregnancy: 50%

Likelihood you will not have a boy this pregnancy: 50%

 

Likelihood you will have no girls if you have 2 children: 1/2 (50%) x 1/2 (50%), so 1/4 (25%).

 

Thus, likelihood you will have at least one girl: 3/4, or 75%.

[TXBeth]

I am not good at probability but I can tell you 16%×12 is actually 1.92% :)

[regentrude]

I am not good at probability but I can tell you 16%×12 is actually 1.92% :)

 

Actually no, it is not. 16% x 12 is 192 %, or 1.92. But not 1.92%. Work it out in decimals if you don't like the % sign:.0.16*12=1.92 which is 192%

 

(and cannot possibly be the answer to the OPs problem since probability cannot exceed 1.)

 

OP: still working on your problem.

[Pegasus]

Ok. Thanks for the tips. Is this closer?

 

Odds you baked on a particular day:  12/30 or 40%

Odds your sister baked on a particular day: 12/30 or 40%

Odds you both baked on a particular day: 40% x 40% = 16%

Odds that you did NOT both bake on a particular day: 84%

 

How do I then account for the fact that there was 30 days that you had a 84% probability that you didn't both bake?  Is this correct:

 

84%^30=0.535%  This extremely small percentage chance that you didn't both bake on the same day during the month.

 

So, 100%-0.535% = 99.465% would be the probability that you did bake on the same day in those 30 days. 

 

 

 

Edited September 16, 2017 by Pegasus

[regentrude]

Ok. Thanks for the tips. Is this closer?

 

Odds you baked on a particular day:  12/30 or 40%

Odds your sister baked on a particular day: 12/30 or 40%

Odds you both baked on a particular day: 40% x 40% = 16%

Odds that you did NOT both bake on a particular day: 84%

 

How do I then account for the fact that there was 30 days that you had a 84% probability that you didn't both bake?  Is this correct:

 

84%^30=0.535%  This extremely small percentage chance that you didn't both bake on the same day during the month.

 

So, 100%-0.535% = 99.465% would be the probability that you did bake on the same day in those 30 days. 

 

yes, that is how I would do it

[Twolittleboys]

Ok. Thanks for the tips. Is this closer?

 

Odds you baked on a particular day:  12/30 or 40%

Odds your sister baked on a particular day: 12/30 or 40%

Odds you both baked on a particular day: 40% x 40% = 16%

Odds that you did NOT both bake on a particular day: 84%

 

How do I then account for the fact that there was 30 days that you had a 84% probability that you didn't both bake?  Is this correct:

 

84%^30=0.535%  This extremely small percentage chance that you didn't both bake on the same day during the month.

 

So, 100%-0.535% = 99.465% would be the probability that you did bake on the same day in those 30 days. 

 

Yep, that's what I came up with as well (but without the nifty notation).

[Pegasus]

Ya'll are awesome! Thanks so much.

[eternalsummer]

I always find these much easier to do if I think through them using something that has both very simple numbers and an obvious solution that I already know intuitively.

 

I know that if you have two kids, you have 50% chance of having a boy and a girl, 25% chance of having just girls (no boys), and 25% chance of having just boys (no girls).

 

So since I know that, I can set up a problem analogous to yours, but with the simpler numbers.  If I set it up the way you did (adding up the probability of the desired scenario for each instance, so in this case the 50% chance of having a girl plus another 50% chance for the second time), it tells me I have a 100% chance of having at least one girl.  I know intuitively that this is wrong, so I try it the other way around.

 

What if I say what is the chance of having no girls?  Well, that's obviously the chance of having one boy times the chance of having another boy, so 25% altogether.  If having no girls is 25% (that would be analogous to you and your sister never baking on the same day), then the chance of having at least one girl is 75%, since that is the other option (either having at least one or having none).