Independent Events (VCE SSCE Mathematical Methods): Quizzes

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Independent Events
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What does it mean for two events AA and BB to be independent?

Pr(AB)=Pr(A)\text{Pr}(A | B) = \text{Pr}(A)

Which formula is the multiplication test for independence?

Pr(AB)=Pr(A)×Pr(B)\text{Pr}(A \cap B) = \text{Pr}(A) \times \text{Pr}(B)

If Pr(A)=0.5\text{Pr}(A) = 0.5, Pr(B)=0.4\text{Pr}(B) = 0.4, and Pr(AB)=0.2\text{Pr}(A \cap B) = 0.2, are AA and BB independent?

No, because 0.20.5×0.40.2 \neq 0.5 \times 0.4

Which is NOT an equivalent condition for independence (when probabilities are non-zero)?

Pr(AB)=Pr(A)+Pr(B)\text{Pr}(A \cup B) = \text{Pr}(A) + \text{Pr}(B)

When are events AA and BB automatically independent?

When Pr(A)=0\text{Pr}(A) = 0 or Pr(B)=0\text{Pr}(B) = 0

Can two events with non-zero probabilities be both independent and mutually exclusive?

No, these concepts are incompatible

For mutually exclusive events, what is Pr(AB)\text{Pr}(A \cap B)?

00

In the coin toss example, what is Pr(second headfirst head)\text{Pr}(\text{second head} | \text{first head})?

12\frac{1}{2}

If Pr(T)=0.75\text{Pr}(T) = 0.75 and Pr(S)=0.25\text{Pr}(S) = 0.25 are independent, what is Pr(TS)\text{Pr}(T \cap S)?

0.18750.1875

Can events be mathematically independent without being physically independent?

Yes, as shown in the dice example

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