An experiment results in one of three mutually exclusive events, A, B, C. it is known that p (A) =.30, p (b) =.55 and p (c) =.15.

A. find each of the following probabilities. 1. P (AUB) 2. P (A∩C) 3. P (A|B) 4. P (BUC) B. Are B and C Independent Events? Explain.

A. 1. P (A∪B) = 0.85

2. P (A∩C) = 0.045

3. P (A/B) = 0.3

4. P (B∪C) = 0.70

B. Event B and Event C are dependent

Step-by-step explanation:

A. As events are mutually exclusive, so,

P (A∪B) = P (A) + P (B)

P (A∩B) = P (A) * P (B)

1. P (A∪B) = ?

P (A∪B) = P (A) + P (B) = 0.3+0.55=0.85

P (A∪B) = 0.85

2. P (A∩C)

P (A∩C) = P (A) * P (C) = 0.30*0.15=0.045

P (A∩C) = 0.045

3. P (A/B)

P (A/B) = P (A∩B) / P (B)

P (A∩B) = P (A) * P (B) = 0.30*0.55=0.165

P (A/B) = P (A∩B) / P (B) = 0.165/0.55=0.3

P (A/B) = 0.3

4. P (B∪C)

P (B∪C) = P (B) + P (C) = 0.55+0.15=0.70

P (B∪C) = 0.70

B.

The event B and C are mutually exclusive and events B and event C are dependent i. e. P (B and C) ≠P (B) P (C)

The events are mutually exclusive i. e. P (B and C) = 0

whereas P (B) * P (C) = 0.55*0.15=0.0825

Mutually exclusive events are independent only if either one of two or both events has zero probability of occurring.

Thus, event B and C are dependent