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Born on a Wednesday


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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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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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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.

 

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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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