rocdocmac 9 Posted January 18, 2018 Report Share Posted January 18, 2018 (edited) 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, 2018 by rocdocmac Changed font Quote Link to post Share on other sites
1 Solution Izzy 1 Posted January 22, 2018 Solution Report Share Posted January 22, 2018 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%. Quote Link to post Share on other sites
0 Molly Mae 103 Posted January 18, 2018 Report Share Posted January 18, 2018 (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. Quote Link to post Share on other sites
0 rocdocmac 9 Posted January 19, 2018 Author Report Share Posted January 19, 2018 @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 Quote Link to post Share on other sites
0 Molly Mae 103 Posted January 19, 2018 Report Share Posted January 19, 2018 In that case: (1/7)^3*(6/7)^2=0.00214196465 Quote Link to post Share on other sites
0 rocdocmac 9 Posted January 19, 2018 Author Report Share Posted January 19, 2018 @Molly Mae Spoiler You're on the right track, but something is missing from both answers! Quote Link to post Share on other sites
0 Molly Mae 103 Posted January 19, 2018 Report Share Posted January 19, 2018 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 Quote Link to post Share on other sites
0 Molly Mae 103 Posted January 19, 2018 Report Share Posted January 19, 2018 (edited) 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, 2018 by Molly Mae Quote Link to post Share on other sites
0 rocdocmac 9 Posted January 19, 2018 Author Report Share Posted January 19, 2018 (edited) @Molly Mae ... Spoiler Your probability perspective is fine! Your latest answer(s) for (1) is not necessarily on the high side. Edited January 19, 2018 by rocdocmac Additional comment added. Quote Link to post Share on other sites
0 Molly Mae 103 Posted January 19, 2018 Report Share Posted January 19, 2018 1 hour ago, rocdocmac said: @Molly Mae ... Hide contents 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 Quote Link to post Share on other sites
0 rocdocmac 9 Posted January 20, 2018 Author Report Share Posted January 20, 2018 (edited) @Molly Mae ... Spoiler Not 0.01066 Edited January 20, 2018 by rocdocmac to spoiler Quote Link to post Share on other sites
0 rocdocmac 9 Posted January 22, 2018 Author Report Share Posted January 22, 2018 (edited) @Izzy ... Spoiler @Molly Mae ... you were halfway there! Edited January 22, 2018 by rocdocmac Moved to spoiler Quote Link to post Share on other sites
0 Molly Mae 103 Posted January 22, 2018 Report Share Posted January 22, 2018 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. Quote Link to post Share on other sites
Question
rocdocmac 9
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!]
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