Probability

Q1.A die is thrown. E = {3,6} (multiple of 3), F = {2,4,6} (even). Are E and F independent?

• ANo, because they share outcome 6
• BYes, because P(E∩F) = P(E)×P(F)
• CNo, because P(E∩F) ≠ P(E)×P(F)
• DYes, because E∩F = φ

Q2.If P(A|B) = P(B|A), what can we conclude?

• AA ⊂ B but A ≠ B
• BA = B
• CA ∩ B = φ
• DP(A) = P(B)

Q3.Theorem of Total Probability: If {E₁, E₂} partitions S and A is any event, then P(A) =

• AP(E₁|A) + P(E₂|A)
• BP(A|E₁) + P(A|E₂)
• CP(E₁)P(A|E₁) + P(E₂)P(A|E₂)
• DP(A∩E₁) × P(A∩E₂)

Q4.P(S|F) where S is the sample space is equal to:

• A0
• BP(F)
• C1
• D1/2

Q5.Two boxes: Bag I: 4 red, 4 black; Bag II: 2 red, 6 black. One bag chosen randomly, a red ball is drawn. P(from Bag I) is:

• A1/2
• B2/3
• C4/8
• D3/4