




Subscribe to our Youtube Channel - https://you.tube/teachoo
Last updated at Dec. 18, 2018 by Teachoo
Transcript
Misc 12 Suppose we have a four boxes A, B, C and D Containing colored marbles as given below : One of the Boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the Probability that it was drawn from box A? box B? box C ? Let R : Event that a red marble is drawn A : Event that the marble selected is from Box A B : Event that the marble selected is from Box B C : Event that the marble selected is from Box C D : Event that the marble selected is from Box D We need to find out Probability of drawn a marble is drawn from Box A, if it is a red. i.e. P(A|R) Also We need to find out Probability of drawn a marble is drawn from Box B, if it is a red. i.e. P(B|R) Also We need to find out Probability of drawn a marble is drawn from Box C, if it is a red. i.e. P(C|R) So, P(A|R) = (๐(๐ด). ๐(๐ |๐ด))/( ๐(๐ด). ๐(๐ |๐ด) + ๐(๐ต). ๐(๐ |๐ต) + ๐(๐ถ). ๐(๐ |๐ถ) + ๐(๐ท). ๐(๐ |๐ท) ) P(B|R) = (๐(๐ต). ๐(๐ |๐ต))/(๐(๐ด). ๐(๐ |๐ด) + ๐(๐ต). ๐(๐ |๐ต) + ๐(๐ถ). ๐(๐ |๐ถ) + ๐(๐ท). ๐(๐ |๐ท) ) P(C|R) = (๐(๐ถ). ๐(๐ |๐ถ))/(๐(๐ด). ๐(๐ |๐ด) + ๐(๐ต). ๐(๐ |๐ต) + ๐(๐ถ). ๐(๐ |๐ถ) + ๐(๐ท). ๐(๐ |๐ท) ) P(A) : Probability that Box A is selected (Since, Boxes are selected at random) = 1/4 P(R|A) = Probability that a red ball is selected from Box A = 1/10 P(B) : Probability that Box B is selected (Since, Boxes are selected at random) = 1/4 P(R|B) = Probability that a red ball is selected from Box B = 6/10 P(C) : Probability that Box C is selected (Since Boxes are selected at random) = 1/4 P(R|C) = Probability that a red ball is selected from Box C = 8/10 P(D) : Probability that Box D is selected (Since Boxes are selected at random) = 1/4 P(R|D) = Probability that a red ball is selected from Box D = 0/10 Putting value to Equations : P(A|R) = (๐(๐ด). ๐(๐ "|" ๐ด))/( ๐(๐ด). ๐(๐ "|" ๐ด) + ๐(๐ต). ๐(๐ "|" ๐ต) + ๐(๐ถ). ๐(๐ "|" ๐ถ) + ๐(๐ท). ๐(๐ "|" ๐ท) ) = (1/4 ร 1/10)/( 1/4 ร 1/10 + 1/4 ร 6/10 + 1/4 ร 8/10 + 1/4 ร 0/10 ) = (1/4 ร 1/10)/( 1/4 ร 1/10 [1 + 6 + 8] ) = 1/15 P(B|R) = (๐(๐ต). ๐(๐ "|" ๐ต))/( ๐(๐ด). ๐(๐ "|" ๐ด) + ๐(๐ต). ๐(๐ "|" ๐ต) + ๐(๐ถ). ๐(๐ "|" ๐ถ) + ๐(๐ท). ๐(๐ "|" ๐ท) ) = (1/4 ร 6/10)/( 1/4 ร 1/10 + 1/4 ร 6/10 + 1/4 ร 8/10 + 1/4 ร 0/10 ) = (1/4 ร 1/10 ร (6))/( 1/4 ร 1/10 [1 + 6 + 8] ) = 6/15 = 2/5 P(C|R) = (๐(๐ถ). ๐(๐ "|" ๐ถ))/( ๐(๐ด). ๐(๐ "|" ๐ด) + ๐(๐ต). ๐(๐ "|" ๐ต) + ๐(๐ถ). ๐(๐ "|" ๐ถ) + ๐(๐ท). ๐(๐ "|" ๐ท) ) = (1/4 ร 8/10)/( 1/4 ร 1/10 + 1/4 ร 6/10 + 1/4 ร 8/10 + 1/4 ร 0/10 ) = ((1/4 ร 1/10) ร (8))/((1/4 ร 1/10) [1 + 6 + 8] ) = 8/15 Hence Probability when a red ball drawn : Selecting Box A = P(A|R) = 1/15 Selecting Box B = P(B|R) = 2/5 Selecting Box C = P(C|R) = 8/15
Miscellaneous
Misc 2 Important
Misc 3
Misc 4 Not in Syllabus - CBSE Exams 2021
Misc 5 Important Not in Syllabus - CBSE Exams 2021
Misc 6 Important Not in Syllabus - CBSE Exams 2021
Misc 7 Important
Misc 8 Important
Misc 9 Important Not in Syllabus - CBSE Exams 2021
Misc 10 Important
Misc 11 Important
Misc 12 You are here
Misc 13 Important
Misc 14 Important
Misc 15 Important
Misc 16 Important
Misc 17 Important
Misc 18
Misc 19
About the Author