An urn contains four balls calculus homework help

7. An urn contains four balls: 1 white, 1 green and 2 red. I draw 3 balls with replacement. Find the probability that I did not see all three colors through two different calculations, as specified by (a) and (b) below.

a. Define the event W = {white ball appeared} and similarly for G and R. Use inclusion-exclusion.

b. Use the complement.

8. Assume that Pr(A) = 0.4 and Pr(B) = 0.7. Making no further assumptions on A and B, show that Pr(AB) satisfies 0.1 ≤ Pr(AB) ≤ 0.4.

9. Show that for any events A1, A2… An, Pr(A1 ∪ A2 ∪∪ An) ≤Pn k=1 Pr(Ak)

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