Name: Bally

Who is asking: Student
Level: Secondary

Question: I have this question I don't know how to do

Investors do not invest all their money in the investment predicted to be the best beuause it is too risky. an investor holds shares in three independent cmpanies. company A, Company B, compnay C. an analyst predicts the probability of profit increases for each company as follows. Company A:0.70 Compamy B:0.50 Compnay C:0.65

(a) If the analyst's predictions are true, what is the probability that all three comapanies show a profit incresse?

ANSWER: I try using vin diagram but it did'nt work, I dont know any other ways to solve this question

(b) if the analyst's predictions are true, what is the probability that at least one comany shows a profit increase?

a) If we assume that companies are indendent:
P(A and B and C)=P(A)*P(B)*P(C)= 0.70*0.50*0.65= 0.2275

b) Consider the negation to the event {at least one company shows an increase}. The negation will be {No company shows an increase} and probability of the last event is: (1-0.7)*(1-0.5)*(1-0.65)= 0.0525. Now or original event will have the probiblity 1-0.0525= 0.9475.