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Category > Statistics Posted 18 May 2017 My Price 3.00

Three cards are placed in a box; one is white on both sides

1. Three cards are placed in a box; one is white on both sides, one is black on both sides, and the third is white on one side and black on the other. One card is chosen at random from the box and placed on a table. The (uppermost) face that shows is white. Explain why the probability that the hidden face is black is equal to 1/3 and not 1/2.

2. If Prob{A | B} = Prob{B} = Prob{A ∪ B} = 1/2, are A and B independent?

 

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Status NEW Posted 18 May 2017 08:05 AM My Price 3.00

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file 1495096003-Answer.docx preview (136 words )
1-----------. T-----------hre-----------e c-----------ard-----------s a-----------re -----------pla-----------ced----------- in----------- a -----------box-----------; o-----------ne -----------is -----------whi-----------te -----------on -----------bot-----------h s-----------ide-----------s, -----------one----------- is----------- bl-----------ack----------- on----------- bo-----------th -----------sid-----------es,----------- an-----------d t-----------he -----------thi-----------rd -----------is -----------whi-----------te -----------on -----------one----------- si-----------de -----------and----------- bl-----------ack----------- on----------- th-----------e o-----------the-----------r. -----------One----------- ca-----------rd -----------is -----------cho-----------sen----------- at----------- ra-----------ndo-----------m f-----------rom----------- th-----------e b-----------ox -----------and----------- pl-----------ace-----------d o-----------n a----------- ta-----------ble-----------. T-----------he -----------(up-----------per-----------mos-----------t) -----------fac-----------e t-----------hat----------- sh-----------ows----------- is----------- wh-----------ite-----------. E-----------xpl-----------ain----------- wh-----------y t-----------he -----------pro-----------bab-----------ili-----------ty -----------tha-----------t t-----------he -----------hid-----------den----------- fa-----------ce -----------is -----------bla-----------ck -----------is -----------equ-----------al -----------to -----------1/3----------- an-----------d n-----------ot -----------1/2-----------. -----------2. -----------If -----------Pro-----------b{A----------- | -----------B} -----------= P-----------rob-----------{B}----------- = -----------Pro-----------b{A----------- âˆ-----------ª B-----------} =----------- 1/-----------2, -----------are----------- A -----------and----------- B -----------ind-----------epe-----------nde-----------nt?----------- A-----------nsw-----------er
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