Probability Test

Result

Probability Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

If E and F are independent, then which one of the following is right?

A
P (E|F) =P (E’∪ F)E’ is complement of E

B
P (E|F) = P (F), P (F) ≠ 0

C
P (E|F) = P (E’), P (F) ≠ 0E’ is complement of E

D
P (E|F) = P (E), P (F) ≠ 0

Solution

If E and F are independent, then P (E|F) = P (E), P (F) ≠ 0 .
Question 2
1 / -0

Let (E₁ , E₂,....,E_n) be a partition of a sample space and suppose that each of E₁ , E₂,.....,E_n has nonzero probability. Let A be any event associated with S, then

A
P(A) = P(E₀) P (A|E₁) + P (E₁) P (A|E₂) + ... + P (E_n – 1) P(A|E_n)

B
P(A) = P(E₁) P (A|E₁) + P (E₁) P (A|E₂) + ... + P (E_n) P(A|E_n)

C
P(A) = P(E₂) P (A|E₁) + P (E₂) P (A|E₂) + ... + P (E_n) P(A|E_n)

D
P(A) = P(E₁) P (A|E₁) + P (E₂) P (A|E₂) + ... + P (E_n) P(A|E_n)

Solution

Let {E₁, E₂, ...,E_n) be a partition of a sample space and suppose that each of E₁, E₂, ..., E_n has nonzero probability. Let A be any event associated with S,then P(A) = P(E₁) P (A|E₁) + P (E₂) P (A|E₂) + ... + P (E_n) P(A|E_n) .by addition law of probability.