7. Consider the following scenario:

• Let P(C) = 0.2

• Let P(D) = 0.3

• Let P(C | D) = 0.4

• Part (a)
  Find P(C AND D).

• Part (b)
  Are C and D mutually exclusive? Why or why not?C and D are notmutually exclusive because
  P(C) + P(D) ≠ 1
  .C and D are mutually exclusive because they have differentprobabilities. C and D are not mutually exclusive because
  P(C AND D) ≠ 0
  .There is not enough information to determine if C and D aremutually exclusive.

• Part (c)
  Are C and D independent events? Why or why not?The events are notindependent because the sum of the events is less than 1.The eventsare not independent because
  P(C) × P(D) ≠ P(C | D)
  . The events are not independent because
  P(C | D) ≠ P(C)
  .The events are independent because they are mutuallyexclusive.

• Part (d)
  Find P(D | C).

8. G and H are mutually exclusive events.

• P(G) = 0.5

• P(H) = 0.3

• Part (a)
  Explain why the following statement MUST be false:
  P(H | G) = 0.4.
  The events are mutually exclusive, which means they can be addedtogether, and the sum is not 0.4.The statement is false because P(H| G) =

P(H)

P(G)

• = 0.6. To find conditional probability, divide
  P(G AND H) by P(H)
  , which gives 0.5.The events are mutually exclusive, whichmakes
  P(H AND G) = 0
  ; therefore,
  P(H | G) = 0.

• Part (b)
  Find
  P(H OR G).

• Part (c)
  Are G and H independent or dependent events? Explain

• G and H are dependent events because they are mutuallyexclusive.

• G and H are dependent events because

• P(G OR H) ≠ 1.

• G and H are independent events because they are mutuallyexclusive.

• There is not enough information to determine if G and Hare independent or dependent events.

9.

Approximately 281,000,000 people over age five live inthe United States. Of these people, 55,000,000 speak a languageother than English at home. Of those who speak another language athome, 62.3 percent speak Spanish.

• E = speaks English at home

• E' = speaks another language at home

• S = speaks Spanish at home

Finish each probability statement by matching thecorrect answer.

• Part (a)
  P(E' )
  = ---Select--- 0.1219 0.1957 0.6230 0.8043

• Part (b)
  P(E)
  = ---Select--- 0.1219 0.1957 0.6230 0.8043

• Part (c)
  P(S and E' )
  = ---Select--- 0.1219 0.1957 0.6230 0.8043

• Part (d)
  P(S | E' )
  = ---Select--- 0.1219 0.1957 0.6230 0.8043