Question 3 (2 points) There are two urns containing colored balls. The first urn

Question

Question 3 (2 points) There are two urns containing colored balls. The first urn contains 18 red balls and 47 blue balls. The secon urn contains 50 red balls and 12 blue balls. One of the two urns is randomly chosen (boh urns bave probability 0.5 of being chosen) and then a ball is drawn at random from one of the two urns. If a red balli drawn, what is the probability that it comes from the first urn? (use decimal of 3 significant digits, percentage, in the answer) not Your Answer Question 3 options:

Explanation / Answer

Question - 3 :

First URN : 18 red ball + 47 blue balls = 65 balls
Second URN : 50 red ball + 12 blue balls = 62 balls


P(First URN / Red Ball) = ?

P(First) = P(Second) = 1/2

P(Red/FirstURN) = 18/65
P(Blue/FirstURN) = 47/65
P(Red/SecondURN) = 50/62
P(Blue/SecondURN) = 12/62

P(First URN / Red Ball) = ( 0.5 * 18/ 65 ) / ( (0.5)*(18/ 65) +  (0.5)*(50/ 62) )
  
=> 0.5 * 0.2769 / ( (0.5)*(0.2769) +  (0.5)*(0.8064) )
=> 0.2041

Thus , IF A RED a Ball is drawn then probability that it is from the First URN is 0.2041

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