tag:blogger.com,1999:blog-6894866515532737257.post979198331778574487..comments2024-08-09T23:38:37.150-07:00Comments on Probably Overthinking It: Probability is hardAllen Downeyhttp://www.blogger.com/profile/01633071333405221858noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-6894866515532737257.post-67473247334004551952016-05-06T07:09:32.966-07:002016-05-06T07:09:32.966-07:00For what it's worth, I was one of those who we...For what it's worth, I was one of those who were puzzled (I wouldn't say annoyed) by the apparent mismatch between the question as posed and Scenarios C and D. <br /><br />At the moment, I'm mostly curious about where this is going. All of the calculations in the notebook seem correct to me, and none seem particularly counterintuitive or surprising. I gather that you're building to something surprising, and I look forward to seeing what it is.Ted Bunnhttps://www.blogger.com/profile/12230509214302717664noreply@blogger.comtag:blogger.com,1999:blog-6894866515532737257.post-82289660885084655962016-05-06T06:29:36.554-07:002016-05-06T06:29:36.554-07:00That is correct in Scenario B (where I choose a di...That is correct in Scenario B (where I choose a die once and then roll it repeatedly).Allen Downeyhttps://www.blogger.com/profile/01633071333405221858noreply@blogger.comtag:blogger.com,1999:blog-6894866515532737257.post-39076968221371630872016-05-06T06:26:28.545-07:002016-05-06T06:26:28.545-07:00if A is the event that you have the R-favorable di...if A is the event that you have the R-favorable die, then as above it's probability P(A) after one roll is now 2/3.<br />So P(R) = P(R|A)P(A) + P(R|Ac)P(Ac) = (2/3)*(2/3)+(1/3)*(1/3)=5/9Anonymoushttps://www.blogger.com/profile/10470259780261074552noreply@blogger.comtag:blogger.com,1999:blog-6894866515532737257.post-20624350118115859042016-05-05T14:05:00.275-07:002016-05-05T14:05:00.275-07:00Good so far!
But I added a followup question: wha...Good so far!<br /><br />But I added a followup question: what's the probability that the outcome of the next roll is red, too? Hint: the scenario is deliberately ambiguous.Allen Downeyhttps://www.blogger.com/profile/01633071333405221858noreply@blogger.comtag:blogger.com,1999:blog-6894866515532737257.post-62587387318361480192016-05-05T13:46:48.561-07:002016-05-05T13:46:48.561-07:00In this case, you can straightforwardly calculate ...In this case, you can straightforwardly calculate favorable probability out of total probability, so<br /><br />[ (1/2).(4/6) ] / [ (1/2).(4/6) + (1/2).(2/6) ] <br />= [ 4/6 ] / [ (4/6) + (2/6) ]<br />= [2] / [2 + 1] = 2/3<br /><br />But you already knew that. Anyways, it's nice to be able to comment something; most of your posts are way above my paygrade.Nuñohttps://www.blogger.com/profile/09089984219014317886noreply@blogger.com