1. There are 4 baskets. The first basket has 3 apples and 4 oranges, the second one has 4 apples and 5 mangoes, the third one has 6 Mangoes and 2 bananas and the last one has 7 bananas and 2 apples. If a fruit is randomly chosen from any basket and it comes out to be an apple, then what is the probability that it was taken out from the second basket?

• P(A|1)=3/7
  P(A|2)=4/9
  P(A|3)=0/8
  P(A|4)=2/9
  
  Hence event 1,2,3,4 are the partitions of the sample space.
  
  The probability of choosing an apple, by the law of total probability
  P(A)=P(A|1)P(1)+P(A|2)P(2)+P(A|3)P(3)+P(A|4)P(4)
  =3/7*1/4+4/9*1/4+0/8*1/4+2/9*1/4
  =23/84
  
  By Baye's theorem,
  P(2|A)=P(A|2)*P(2)/P(A)
  =4/9*(1/4)/(23/84)
  =28/69
• 9 years agoHelpfull: Yes(27) No(2)
• probability of choosing 2 nd basket is 1/4 (1 among 4 baskets)
  second basket has 4 apples and total fruits 4 A+5 M =9
  taking apple out is 4/9
  so ans is 1/4 * 4 /9 =1/9
• 9 years agoHelpfull: Yes(25) No(15)
• the probability of selecting a basket is 1/4.
  the probability of selecting an apple from basket 2 is 4c1/9c1*1/4.
  now the probability of selecting an apple from any of the baskets is given by 1/4*3/7+4/9*1/4+1/4*0/8+1/4*2/9.
  finally p(apple from basket 2 )=( 4c1/9c1*1/4)/(1/4*3/7+4/9*1/4+1/4*0/8+1/4*2/9)
  on solving it gives a result of 28/69.
• 9 years agoHelpfull: Yes(6) No(3)
• ..............IMPORTANT.............
  PLZ DONT GET CONFUSED WITH BAYES THEOREM
  
  here bayes theorem is not applicable....
  https://www.youtube.com/watch?v=N0l5NuysZII here u can get the reason why??
  
  the correct ans is 1/4*4/9=1/9.
  
• 8 years agoHelpfull: Yes(4) No(0)
• 1/3
  Bcz only 3 basket have apple
• 9 years agoHelpfull: Yes(2) No(4)
• Ankit Kumar Roy and Tejaswi VVDL have given the answer as 28/69 from basket number 2 and as 23/84 for selecting an apple from any one of the four baskets. How come probability of selecting an apple from basket number 2 is more than selecting an apple from any one of the baskets. It should be less. I agree with the answers of Syam Kumar
• 9 years agoHelpfull: Yes(1) No(1)
• this clear show . item taken then it ask from which bag . so its bays theorem ......go with ankit kumar's ans
• 6 years agoHelpfull: Yes(1) No(0)
• since an apple is already selected then we have to calculate the probability of it's belongingness to 2nd basket.
  ans is 4/9.
  
• 9 years agoHelpfull: Yes(0) No(5)
• 4/9 as 4c1/9c1
• 9 years agoHelpfull: Yes(0) No(5)
• P(C3/H)= P(C3) P(H/C3) / (P(H) -> 1/3 * 1/2 / (1/3*1+1/3*0+1/3*1/2) ->1/3
• 6 years agoHelpfull: Yes(0) No(0)
• 45/69
  total by apples
• 6 years agoHelpfull: Yes(0) No(0)