# Misc 12

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 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 ? • 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) = 𝑃 𝐴. 𝑃(𝑅|𝐴) 𝑃 𝐴. 𝑃 𝑅|𝐴 + 𝑃 𝐵. 𝑃 𝑅|𝐵 + 𝑃 𝐶. 𝑃 𝑅|𝐶 + 𝑃 𝐷. 𝑃 𝑅|𝐷 P(B|R) = 𝑃 𝐵. 𝑃(𝑅|𝐵)𝑃 𝐴. 𝑃 𝑅|𝐴 + 𝑃 𝐵. 𝑃 𝑅|𝐵 + 𝑃 𝐶. 𝑃 𝑅|𝐶 + 𝑃 𝐷. 𝑃 𝑅|𝐷 P(C|R) = 𝑃 𝐶. 𝑃(𝑅|𝐶)𝑃 𝐴. 𝑃 𝑅|𝐴 + 𝑃 𝐵. 𝑃 𝑅|𝐵 + 𝑃 𝐶. 𝑃 𝑅|𝐶 + 𝑃 𝐷. 𝑃 𝑅|𝐷 Putting value to Equations : P(A|R) = 𝑃 𝐴. 𝑃(𝑅|𝐴) 𝑃 𝐴. 𝑃 𝑅|𝐴 + 𝑃 𝐵. 𝑃 𝑅|𝐵 + 𝑃 𝐶. 𝑃 𝑅|𝐶 + 𝑃 𝐷. 𝑃 𝑅|𝐷 = 14 × 110 14 × 110 + 14 × 610 + 14 × 810 + 14 × 010 = 14 × 110 14 × 110 [1 + 6 + 8] = 115 P(B|R) = 𝑃 𝐵. 𝑃(𝑅|𝐵) 𝑃 𝐴. 𝑃 𝑅|𝐴 + 𝑃 𝐵. 𝑃 𝑅|𝐵 + 𝑃 𝐶. 𝑃 𝑅|𝐶 + 𝑃 𝐷. 𝑃 𝑅|𝐷 = 14 × 610 14 × 110 + 14 × 610 + 14 × 810 + 14 × 010 = 14 × 110 × 6 14 × 110 [1 + 6 + 8] = 615 P(C|R) = 𝑃 𝐶. 𝑃(𝑅|𝐶) 𝑃 𝐴. 𝑃 𝑅|𝐴 + 𝑃 𝐵. 𝑃 𝑅|𝐵 + 𝑃 𝐶. 𝑃 𝑅|𝐶 + 𝑃 𝐷. 𝑃 𝑅|𝐷 = 14 × 810 14 × 110 + 14 × 610 + 14 × 810 + 14 × 010 = 14 × 110 × 8 14 × 110 [1 + 6 + 8] = 815 Hence Probability when a red ball drawn : Selecting Box A = P(A|R) = 115 Selecting Box B = P(B|R) = 215 Selecting Box C = P(C|R) = 815

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.