Ask Question
10 July, 23:16

If A, B, and C are mutually exclusive events with P (A) 0.2, P (B) : 0.3, and P (C) 0.4, determine the following probabilities:

a. P (A U B U C)

b. P (A∩B∩C)

c. P (A∩B)

d. P[ (AUB) ∩C]

e. P (A'∩B'∩ C')

+3
Answers (1)
  1. 10 July, 23:38
    0
    a. 0.9

    b. 0.024

    c. 0.06

    d. 0.2

    e. 0.336

    Step-by-step explanation:

    Since A, B and C are mutually exclusive then P (A U B U C) = P (A) + P (B) + P (C) and P (A∩B∩C) = P (A) * P (B) * P (C).

    a.

    P (A U B U C) = P (A) + P (B) + P (C)

    P (A U B U C) = 0.2+0.3+0.4=0.9

    b.

    P (A∩B∩C) = P (A) * P (B) * P (C)

    P (A∩B∩C) = 0.2*0.3*0.4=0.024

    c.

    P (A∩B) = P (A) * P (B)

    P (A∩B) = 0.2*0.3=0.06

    d.

    P[ (AUB) ∩C]=P (AUB) * P (C)

    P (AUB) = P (A) + P (B) = 0.2+0.3=0.5

    P[ (AUB) ∩C]=0.5*0.4=0.20

    e.

    P (A') = 1-P (A) = 1-0.2=0.8

    P (B') = 1-P (B) = 1-0.3=0.7

    P (C') = 1-P (C) = 1-0.4=0.6

    P (A'∩B'∩ C') = P (A') * P (B') * P (C')

    P (A'∩B'∩ C') = 0.8*0.7*0.6=0.336
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “If A, B, and C are mutually exclusive events with P (A) 0.2, P (B) : 0.3, and P (C) 0.4, determine the following probabilities: a. P (A U B ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers