Question

8) CHALLENGE QUESTION A probability experiment has exactly four mutually exclusive outcomes: W,X,Y & Z. The following is true: • P(W) = 4P(X) • P(X) = P(Y) - P(Z) • P(W) = P(X) + P(Y) + 5P(Z) Find the four probabilities P(W), P(X), P(Y), P(Z)

Answer 1

87 Since the experiment has exactly 4 mustually exclusive events, so, P(WUXU YOZ) 1 = P(W) +P(x)+ P(x)+P(2).' Let P(x)= a , P(w)=4a .: P(V)-P(z) > a = P(x) - P(x) + P(1) +5 P(Z) = P(W) = P() + 5 P(x) = 32 - 6 - From +6 = P(*)+a+5P(2) = 30 7 6 P(z)= 2a 7 P(z)= - P(Y) = 1 a ta alla 2

.: P(x)+ P(x)+ P(z)+P(w) = 1 + a+ya+ba+40=1 20 231 paste = P(19) Žo, P(1) - Š - P(z) ==ó - P(w) =