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# Born on a Wednesday

## Question

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 by rocdocmac
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## Recommended Posts

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(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.

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@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

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In that case:

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

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@Molly Mae

Spoiler

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

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2 hours ago, rocdocmac said:

@Molly Mae

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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

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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 by Molly Mae

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@Molly Mae ...

Spoiler

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

Edited by rocdocmac

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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

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@Molly Mae ...

Spoiler

Not 0.01066

Edited by rocdocmac
to spoiler

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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%.

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@Izzy ...

Spoiler

@Molly Mae ...  you were halfway there!

Edited by rocdocmac
Moved to spoiler

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11 hours ago, rocdocmac said:

@Izzy ...

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@Molly Mae ...  you were halfway there!

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

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