## Ashish Bajpai is teaching live on Unacademy Plus

BAYES THEOREM Let S be the Somple space and set E,E En be 7 mutualy exclusive and exhaustive events associated cith a ran dom exHnimerA w A is ary ev Or or Em then

Proo YoO En one m mutually ex clusiue and exhaustive cvents, we have

ty addition theorem P (EL)

An En oco im m Oe have

PCA) Ec) p CA) E c

0 1 Note nedoned to as ( hypothe sis) and the robaliAHics Priori To bobilidies as they exist efore e the events E, E2, En ane asuae CEn) ae known as the

No+e p(n/EQ=1' 2,3'--.7) pio babtis as the broba bilities one calld the likely hood the tei hoa consi denation Occars given each and eva proi probaHies

In a bol factory machines A and Cmanafactune espectively 2.5.1. 3sl. and 4ot of the tota0 bol their oukfut S, 4 and 2 pncent ar enesbectively defective bolts . A baut i s dnacon at random from the bro du ct ut is manactured the machine

lo lo o 4- 4 6 S