Use the diagram to determine the probabilities: a) P(A) _____ b) P(AUBUC) _____

Question

Use the diagram to determine the probabilities: a) P(A) _____ b) P(AUBUC) _____ c) P[A Intersection C] _____ d) P[C|A] _____ e) P[C|(A Union B)] Union Four identical bowls are labeled 1, 2, 3, and 4. Bowl 1 has 5 white chips. Bowl 2 has 3 white chips and 3 black chips. Bowl 3 has 1 white chip and 3 black chips. Bowl 4 has 2 white chips and 4 black chips. Bowl 1: WWWWW Bowl 2: WWWBBB Bowl 3: WBBB Bowl 4: WWBBBB A bowl is randomly selected and then 2 chips are selected. Determine the probability that both chips are white. Show your work.

Explanation / Answer

(According to Chegg policy, either a maximum of four subquestions or one question containing four subquestions will be answered. Please post the remaining in another question)

6. From the figure

a) P(A) = 0.04 + 0.06 + 0.05 + 0.15 = 0.3

b) P(A U B U C) = 0.15

c) P(A C) = 0.15 + 0.05 = 0.2

d) P(C|A) = P(A C) / P(A) = 0.2 / 0.3 = 0.67

e) P(A U B) = 0.04 + 0.21 + 0.06 + 0.15 + 0.02 + 0.05

= 0.53

P(C|[A U B]) = P(A U B U C) / P(A U B)

= 0.15 / 0.53

= 0.283

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