Question

Let and B be events in a sample space S, and let C = S - (AUB). Suppose P(A) = 0.8, P(B) = 0.2, and P(An B) = 0.1. Find each of the following. (a) P(AUB) (b) P(C) (c) PAS (d) PLAC BC) (e) PLACUBS (1) P(BCnc)

Answer 1

& Soins Griver that A and B be events in a sample spaces and C= S-AUB) (i.. C = CAUBC) also, P(A) = 0.8 P(B) = 0.2 and PLANB) = 0.1 we have to find P(AUB), PCC) , PLA), PLANBO) PAGUBC) and Ponc). 9 B ANB) 0.9 PAUB) = PA) + P(B) —P(ANB) » P(AUB) = 0.8 + 0.2 - 0.1 P(AUB) PC) = PLAUBJC)= 1 - P(AUB) (3°C (Augf given PC) = 1 - P (AUB) > PC) 1-0.9 (PUB=0.9 from ) » TPC) = 0.1 P(A) = 1 - P(A) PA) = 1-0.8 (.'P(A) = 0+R(fiven) > IP(AC) = = 0.2 PAOBC) = P(ABC) > PAN) 1 - P(AUB) PLANG) z 1-0.g IPCANE) 0. (PAUR) cage forma)

PCACUB - P(ANBJC) & PLAUB) = 1- PLANB) > PLAUBC) - 0.1 (: PONE) = 0.1 (given) I PLAUB) 0.9 since, C CBC Then, Bencec 5 POBOC)= PC) P(Benc) = PAUBS) P(BNC) 2 - P(AUB) P(BOC)2 1-0.9 । PLAUB) Fog farma 3 PLESNC) = 0 h

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