Class Neten: an.pat 20, 7. x % 7.5-76Cardleral Pobatir x c www w.bassgn Assignme

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Class Neten: an.pat 20, 7. x % 7.5-76Cardleral Pobatir x c www w.bassgn Assignment-Responseslas?dep 1659893o Acontains hve white balls and fw black balls. urn contains six white balls and seven black balls. A bal is drawn frn um A·d ten trad erred tourn 8. A ball is then drawn from Urn 8. Whet is the probablity that the transferred ball was black given that the second ball drawn was black? (Round your anewer to three decimal places 500 ikely Democratic voters and 300 skely Republican voters asked the question: Do you support or oppose legisjation that would require trigger locks on guns, to prevent misuse by children? The folowing results were obtained Democrats- Republicans,% y chosen responde" the survey answered "support," what is the prebab ity that he or she-·ley Repubican voter, Round your ans to three decimal places.) Submiat Assigrment Save Assignment Progness MacBook Air 20 0

Explanation / Answer

Question 13:

Here we are given that:

Urn A: five white and four black balls

Urn B: six white and seven black balls

Now using law of total probability we get here: ,

P( second draw is black ) = P( second draw is black | first draw is black ) P( first draw is black ) + P( second draw is black | first draw is white ) P( first draw is white )

P( second draw is black ) = (8/14)*(4/9) + (7/14)*(5/9) = 0.5317

Now the required probability that the first ball was black given that the second ball drawn is black is computed as:

P( first draw is black | second draw is black ) = P( second draw is black | first draw is black ) P( first draw is black ) / P( second draw is black )

P( first draw is black | second draw is black ) = (8/14)*(4/9) / 0.5317 = 0.4776

Therefore 0.478 is the required probability here. ( rounded to three decimal places )

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