1. Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If A and B are independent events with P(A) ≠ 0 and P(B) ≠ 0, then A ∩ B ≠ Ø.
2. Let E be any event in a sample space S.
(a) Are E and S independent?
(b) Are E and Ø independent?
3. According to a survey conducted in 2004 of 1000 American adults with Internet access, one in four households plan to switch ISPs in the next 6 months. Of those who plan to switch, 2% of the households are likely to switch to a satellite connection, 29% to digital subscriber line (DSL), 28% to cable modem, 35% to dial-up modem, and 6% don't know which service provider they will switch to. (Round your answers to three decimal places.)
(a) What is the probability that a randomly selected survey participant is planning to switch ISPs to a dial-up modem connection?
(b) If a person in the survey has planned to switch ISPs, what is the probability that he or she will upgrade to high-speed service (DSL, satellite, or cable)?
Answers to any of these would be greatly appreciated
10pts to best answer
If A and B are independent events with P(A) ≠ 0 and P(B) ≠ 0, then A ∩ B ≠ Ø.
2. Let E be any event in a sample space S.
(a) Are E and S independent?
(b) Are E and Ø independent?
3. According to a survey conducted in 2004 of 1000 American adults with Internet access, one in four households plan to switch ISPs in the next 6 months. Of those who plan to switch, 2% of the households are likely to switch to a satellite connection, 29% to digital subscriber line (DSL), 28% to cable modem, 35% to dial-up modem, and 6% don't know which service provider they will switch to. (Round your answers to three decimal places.)
(a) What is the probability that a randomly selected survey participant is planning to switch ISPs to a dial-up modem connection?
(b) If a person in the survey has planned to switch ISPs, what is the probability that he or she will upgrade to high-speed service (DSL, satellite, or cable)?
Answers to any of these would be greatly appreciated
10pts to best answer
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If A and B are independent events
P(A ∩ B) = P(A).P(B)
Since P(A) ≠ 0 and P(B) ≠ 0, we have P(A ∩ B) ≠ 0.
2) Both a) and b) hold. It can be shown using definition of independence:
A and B are independent iff P(A ∩ B) = P(A).P(B)
3)a) 0.25*0.35
b) 0.59
P(A ∩ B) = P(A).P(B)
Since P(A) ≠ 0 and P(B) ≠ 0, we have P(A ∩ B) ≠ 0.
2) Both a) and b) hold. It can be shown using definition of independence:
A and B are independent iff P(A ∩ B) = P(A).P(B)
3)a) 0.25*0.35
b) 0.59