Born on a Wednesday

[rocdocmac 3]

The probability that any one person selected at random was born on a Wednesday, is 0.1429 (~14 %).

 

What is the probability that of any …

(1)   Seven persons chosen at random, exactly one was born on a Friday?

(2)   Five persons chosen at random, three were born on a Sunday?

 

[Mr Moderator, if this question has appeared before, please remove it!]

 

 

 

 

Edited January 18 by rocdocmac
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[Izzy 0]

Let's see if I remember some probability. 

I assume a 14% chance of being born on any given day of the week. 

1) The probability that exactly one person out of seven is born on a Friday is 7 * (.14) * .86^6 = 39.6%. 

2) The probability that three out of five people are born on a Sunday is (5 choose 3) * .14^3 * .86^2 = 2%. 

[Molly Mae 103]

(1)

(6/7)^6*1/7=0.05665272286

(2)

For (2), I'll assume "at least three" since (1) specified "exactly one".

(1/7)^3+(1/7)^4+(1/7)^5=0.00339144404

But as I always say, probability is probably not my forte.

[rocdocmac 3]

@Molly Mae ... 

Spoiler

For (2), I'll assume "at least three" since (1) specified "exactly one".

(1/7)^3+(1/7)^4+(1/7)^5=0.00339144404

But as I always say, probability is probably not my forte.

EXACTLY 3

 

 

[Molly Mae 103]

In that case:

(1/7)^3*(6/7)^2=0.00214196465

[rocdocmac 3]

@Molly Mae

Spoiler

You're on the right track, but something is missing from both answers!

 

[Molly Mae 103]

2 hours ago, rocdocmac said:

@Molly Mae

  Hide contents

You're on the right track, but something is missing from both answers!

 

I'm hoping it's something from a probability perspective.  I assume an equal likelihood of being born on any day of the week.  I don't know if I need to state that assumption.

As I mentioned before, I'm not terribly great at this.

Is it perhaps that I calculated for (1) the probability that a specific person was born on a Friday?  If that's the case, perhaps (1) should be 0.39656906002.  But 40% seems a bit high.  It makes sense in my head logically, but the answer just seems a bit too high.  You can see that I'm a bit out of my element.  =P

[Molly Mae 103]

27 minutes ago, Molly Mae said:

I'm hoping it's something from a probability perspective.  I assume an equal likelihood of being born on any day of the week.  I don't know if I need to state that assumption.

As I mentioned before, I'm not terribly great at this.

 

  Reveal hidden contents

Is it perhaps that I calculated for (1) the probability that a specific person was born on a Friday?  If that's the case, perhaps (1) should be 0.39656906002.  But 40% seems a bit high.  It makes sense in my head logically, but the answer just seems a bit too high.  You can see that I'm a bit out of my element.  =P

 

Yeah, I'm pretty sure the above can't be right.

 

Perhaps 0.33518439994 is closer to the answer.

EDIT: But that still seems pretty high, in my mind.

Edited January 19 by Molly Mae

[rocdocmac 3]

@Molly Mae ...

Spoiler

Your probability perspective is fine! Your latest answer(s) for (1) is not necessarily on the high side.

 

Edited January 19 by rocdocmac
Additional comment added.

[Molly Mae 103]

1 hour ago, rocdocmac said:

@Molly Mae ...

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Your probability perspective is fine! Your latest answer(s) for (1) is not necessarily on the high side.

 

In that case, a revised #2:

0.0106640413

[rocdocmac 3]

@Molly Mae ...

Spoiler

Not 0.01066

 

Edited January 20 by rocdocmac
to spoiler

[rocdocmac 3]

@Izzy ...

Spoiler

@Molly Mae ...  you were halfway there!

Edited January 22 by rocdocmac
Moved to spoiler

[Molly Mae 103]

11 hours ago, rocdocmac said:

@Izzy ...

  Hide contents

@Molly Mae ...  you were halfway there!

This is absolutely something I should have been able to reason myself into.  D'oh.