Could you please provide the work for the solution? Thank You Frodo, Samwise and
ID: 3271455 • Letter: C
Question
Could you please provide the work for the solution? Thank You
Frodo, Samwise and Pippin arc 3 "happy go lucky" teenagers. One day they find radioactive ring in their village lake. This ring has to be immediately disposed off into a fiery volcano since an evil CEO has his "eye" (literally) set on this ring. They take it back to their village and ask the remaining villagers to help them plan what to do. In the remaining village: 7 do not want to send out a group that disposes off the ring at all. They want everything to stay as is. Out of the remaining villagers: 35 want at least Frodo to be part of the group that disposes off the ring: 21 want at least Samwise to be part of the group that disposes off the ring: 28 want at least Pippin to be part of the group that disposes off the ring: When these villagers were questioned further: 7 of the villagers wanted at least Frodo and Sam to be part of the group: 9 of the villagers wanted at least Frodo and Pippin to be part of the group: 6 of the villagers wanted at least Sam and Pippin to be part of the group: When the villagers were pressed even further, there were only 3 people who wanted all 3 of Frodo, Sam and Pippin to go. If you picked a villager at random (not Frodo, Sam or Pippin but the above collection who were polled), what is the chance that you picked someone who wanted a group of exactly 2 of the three finders of the ring, to go dispose off the radioactive ring? Simplify your answer so it looks like a fraction without any factorials (e.g. 12/25).Explanation / Answer
A - Frodo ,
B -Sam
C -Pippin
n(A) = 35 n(B) = 21, n(C) = 28
n (AB) = 7 n (AC) =9, n (CB) = 6
n (A B C) = 3
n (A U B U C) = n (A)+n (B)+n (C)-n (AB)-n (BC)-n (AC)+n (A B C)
hence
n (A U B U C) = 35 +21+ 28 - 7-9-6 + 3
= 65
number of villager who wanted a group of exactly 2 = n (AB)+n (BC)+n (AC)-3* n (A B C)
=7+9+6 - 3*3
= 13
hence required answer = 13/(65+7) = 13/72