# Question

Show by means of numerical examples that P(B| A) + P(B| A')

(a) May be equal to 1;

(b) Need not be equal to 1.

(a) May be equal to 1;

(b) Need not be equal to 1.

## Answer to relevant Questions

Duplicating the method of proof of Theorem 2.10, show that P(A ∩ B ∩ C ∪ D) = P(A) · P(B| A) · P(C| A ∩ B) · P(D| A ∩ B ∩ C) provided that P(A ∩ B ∩ C) ≠ 0. Refer to Figure 2.10 to show that P(A ∩ B ∩ C) = P(A) · P(B) · P(C) does not necessarily imply that A, B, And C are all pairwise independent. Figure 2.10 Show that P(A ∪ B) ≥ 1- P(A') - P(B') for Any two events A And B defined in the sample space S. An experiment consists of rolling a die until a 3 appears. Describe the sample space And determine (a) How many elements of the sample space correspond to the event that the 3 appears on the kth roll of the die; (b) How ...An experiment has five possible outcomes, A, B, C, D, And E, that are mutually exclusive. Check whether the following assignments of probabilities are permissible And explain your Answers: (a) P(A) = 0.20, P(B) = 0.20, P(C) ...Post your question

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