Question

Suppose we have a late-night bus and towards the end of the route, there are 3 passengers {P1, P2, P3} and 5 stops {S1, S2, S3, S4, S5} remain. Suppose further that each passenger is inebriated and is thus is equally likely to get off at any one of the stops. (i) We wish to list the set of outcomes in the sample space each of whose outcomes is an ordered triple of all three Sij for I-1,2,3, where Sij means that passenger Pi got off at the stop Sj a Write the outcome that P1 and P2 debarked at S4, and P3 debarked at S1. HINT: Its form is (-, --, --) where each - is an integer from 1 to 5 b) How many outcomes are in our sample space? (ii) Using (), find the probability that no two of our passengers got off at the same stop (iii) There will definitely be a fight if exactly two passengers get off at any given stop. (If nobody or 1 passenger gets off at a stop, there is nobody to fight with, and if all three get off at the same stop, one guy will talk the other two out of fighting.) So, what is the probability of a fight occurring? passengers (iv) Finally, suppose there are n stops remaining, and k< n Answer question (ii) now

Answer 1

Solution 5 stops (sI, S2,83, Sq, S5), (P. P2 P) andd There are 3 passenger a) utcomes that PI and pa dehar Ked at s4 and p3 debarked at9 b) Total numbey of autcomes in sarmplc space XSX5X5 3 195 Poobability that no two of our passengeis got ff at game Stop we have total 5 Stopg e, passenger gels off m any one of etop then pasgengey 2 we have 4 stops ond or passenger 3 we have Temaning 3 stop two eu passergeis got of at he same stop 5xyx3 Hence no Hence equiTed podbabil?ty that no two or ou possengers got of at the game stop SxYx3 048 53 1pobability that no tw04 On Poobabity of o feght occumng passengers got of at the game Sop -0.48 0.5a

at the orne Grop passergeng got 1- ntn-)(n-kll). (n-1)(n-KU)