Probability Q's: Plz Help!

[DentalP87]

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1) Say that there are 9 doors of which 6 have cars and 3 have goats. You and your friend get to open a door for the prize (car or goat). Would it be your best interest to open the door first or 2nd?

2) Say there are two well-shuffled 52 card decks. We turn over cards simultaneously from both decks until there are no cards left. What is the probability that there are NO matches out of the 52 turns?

3) Given 16 peeps, what is the probability that among the 12 months in the year there are 3 months containing exactly 4 birthdays each and there are 2 months containing exactly 2 birthdays each?

These are tough questions I know.. help will be much appreciated. thanks!

 

[klutzy1987]

1) Say that there are 9 doors of which 6 have cars and 3 have goats. You and your friend get to open a door for the prize (car or goat). Would it be your best interest to open the door first or 2nd?

According to Monty Hall it would be in your best interest to open the second door. However I am certain that Monty Hall is a fool and have proven his trheory wrong. There is no difference which door you open.

 

[DentalP87]

According to Monty Hall it would be in your best interest to open the second door. However I am certain that Monty Hall is a fool and have proven his trheory wrong. There is no difference which door you open.

mm ok. thanks.

Any math guys out there??

 

[Streetwolf]

1) I get no difference but the question makes it seem like there should be a difference. Maybe I'm reading it incorrectly.

The Monty Hall problem is different because the host eliminates a door for you and he KNOWS which door has the car behind it. In that case you SHOULD switch. Nothing here indicates any knowledge of what's behind whatever door is being opened first.

2) I get [1 - (1/2!) - (2/3!) - (3/4!) - (4/5!) - ... - (49/50!) - (51/52!)] which is a really small decimal. The percentage is that multiplied by 100. If that's wrong I'll take another stab at it. I don't have two decks of cards with me to confirm that you have a match > 99.999 whatever% of the time. Seems very high but it might be right.

3) I'll tackle later. This wouldn't be as bad if the months had the same freakin' number of days.

 

[doc3232]

1) I get no difference but the question makes it seem like there should be a difference. Maybe I'm reading it incorrectly.

The Monty Hall problem is different because the host eliminates a door for you and he KNOWS which door has the car behind it. In that case you SHOULD switch. Nothing here indicates any knowledge of what's behind whatever door is being opened first.

2) I get [1 - (1/2!) - (2/3!) - (3/4!) - (4/5!) - ... - (49/50!) - (51/52!)] which is a really small decimal. The percentage is that multiplied by 100. If that's wrong I'll take another stab at it. I don't have two decks of cards with me to confirm that you have a match > 99.999 whatever% of the time. Seems very high but it might be right.

3) I'll tackle later. This wouldn't be as bad if the months had the same freakin' number of days.

For number 1:

I think this is what will happen. Your friend opens a door, so there is a 2/3 chance he gets a car and a 1/3 chance he gets goat. This changes the number of cars and doors now.

2/3 * 5/8
1/3 * 6/8


Add these together to get the prob of getting a car going after your friend chooses.
And it adds up to .6666667
I was expecting a difference...but meh. This is the math behind it anyway.

 

[DentalP87]

wow guys thanks! realy appreciate it😉

 

[DentalP87]

1) I get no difference but the question makes it seem like there should be a difference. Maybe I'm reading it incorrectly.

The Monty Hall problem is different because the host eliminates a door for you and he KNOWS which door has the car behind it. In that case you SHOULD switch. Nothing here indicates any knowledge of what's behind whatever door is being opened first.

2) I get [1 - (1/2!) - (2/3!) - (3/4!) - (4/5!) - ... - (49/50!) - (51/52!)] which is a really small decimal. The percentage is that multiplied by 100. If that's wrong I'll take another stab at it. I don't have two decks of cards with me to confirm that you have a match > 99.999 whatever% of the time. Seems very high but it might be right.

3) I'll tackle later. This wouldn't be as bad if the months had the same freakin' number of days.

for 3 u assume there are same number of days in each month. soryr bout that

 

[DentalP87]

1) I get no difference but the question makes it seem like there should be a difference. Maybe I'm reading it incorrectly.

The Monty Hall problem is different because the host eliminates a door for you and he KNOWS which door has the car behind it. In that case you SHOULD switch. Nothing here indicates any knowledge of what's behind whatever door is being opened first.

2) I get [1 - (1/2!) - (2/3!) - (3/4!) - (4/5!) - ... - (49/50!) - (51/52!)] which is a really small decimal. The percentage is that multiplied by 100. If that's wrong I'll take another stab at it. I don't have two decks of cards with me to confirm that you have a match > 99.999 whatever% of the time. Seems very high but it might be right.

3) I'll tackle later. This wouldn't be as bad if the months had the same freakin' number of days.

oh yea for 2 it has exact match means exactly an ace of hearts with an ace of hearts, for example

 

[Streetwolf]

oh yea for 2 it has exact match means exactly an ace of hearts with an ace of hearts, for example

Yeah I know.

 

[Streetwolf]

I think for #3 you first choose the 6 months you are working with, except remember that ORDER MATTERS. The 6 months could be Jan through June but there's a difference between the 4 people sharing a Jan birth month or those same 4 people sharing a June birth month.

So you do (12 P 6) which is 12! / (12-6)! which is 12*11*10*9*8*7.

Then each person has a 1/12 chance of being born in any given month. With 16 people that's 12^16.

Do (12 P 6) over 12^16 and get 3.6 x 10^-10 %.

Pretty low 🙂

I guess that's because there are just SO many ways to place 16 people into 12 months.