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What is the difference between the multiplication rule for independent versus dependent events?
Given two events, A and B, Pr(A and B) = Pr(A)*Pr(B) if A and B are independent and Pr(A and B) = Pr(A | B)*Pr(B) if they are not.
What is the probability of obtaining exactly three heads in four flips of a coin given that at least two are heads?
Pr(3H given >= 2H) = Pr(3H and >= 2H)/Pr(>=2H) = Pr(3H)/Pr(>=2H) = (1/4)/(11/16) = 4/11.
What is the probability of rolling two fair value dice getting two different numbers?
Pr(Two different numbers) = 1 - Pr(Two same) = 1 - 1/6 = 5/6 = 83.3%
What is the describing of the complementary event and find its probability?
Suppose there is an event A and the probability of A happening is Pr(A). Then the complementary event is that A does not happen or that "not-A" happens: this is often denoted by A'.Then Pr(A') = 1 - Pr(A).Suppose there is an event A and the probability of A happening is Pr(A). Then the complementary event is that A does not happen or that "not-A" happens: this is often denoted by A'.Then Pr(A') = 1 - Pr(A).Suppose there is an event A and the probability of A happening is Pr(A). Then the complementary event is that A does not happen or that "not-A" happens: this is often denoted by A'.Then Pr(A') = 1 - Pr(A).Suppose there is an event A and the probability of A happening is Pr(A). Then the complementary event is that A does not happen or that "not-A" happens: this is often denoted by A'.Then Pr(A') = 1 - Pr(A).
What is the probability when two people alternately are picking first from a class with 12 girls and 13 boys and then from a class with 10 boys and 11 girls that the first will pick two girls first?
The fact that the two people are picking alternately first from one class and then from the second means that the first picker always has first selection from whoever is remaining in each class; thus for the first picker: pr(1st girl) = 12/(12+13) = 12/25 Pr(2nd girl) = 11/(11+10) = 11/21 → Pr(two girls picked) = pr(1st girl) × pr(2nd girl) = 12/25×11/21 = 44/175
