3 [10 points A survey of engineering firms reveals that 80% have their own mainf

Question

3 [10 points A survey of engineering firms reveals that 80% have their own mainframudak anticipate purchasing a mainframe computer in the near future (B), and 5% puter (M), 10% have a mainfram (a) Find the probability e computer and anticipate buying another in the near future that a randomly selected firm has a mainframe computer or antich pates purchasing one in the near future. (b) Find the probability that a randomly selected firm does not have a mainframe computer and does not anticipate purchasing one in the near future. (c) Find the probability that a randomly selected firm has a mainframe computer but does not anticipate purchasing one in the near future. ven that (d) Find the probability that a randomly selected firm has a mainframe computer gi it anticipates purchasing one in the near future (e) Are the events "having a mainframe computer" and "anticipate purchasing a mainframe computer in the near future" independent? Justify your answer using probabilities.

Explanation / Answer

Ans:

P(M)=0.8

P(B)=0.1

P(M and B)=0.05

a)P(M or B)=P(M)+P(B)-P(M and B)=0.8+0.1-0.05=0.85

b)P(neither M nor B)=1-P(M or B)=1-0.85=0.15

c)P(M and Bc)=P(M)-P(M and B)=0.8-0.05=0.75

d)P(M/B)=P(M and B)/P(B)=0.05/0.1=0.5

e)For M and B to be independent,

P(M and B)=P(M)*P(B)

But

P(M and B)=0.05

P(M)*P(B)=0.8*0.1=0.08

As,both are not equal,so M and B are not independent.

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