Consider the following scenario: • Let P ( C ) = 0.4 • Let P ( D ) = 0.5 • Let P

ID: 3021221 • Letter: C

Question

Consider the following scenario:

• Let P(C) = 0.4
• Let P(D) = 0.5
• Let P(C | D) = 0.6

1.) Find P(C AND D).

2.) Are C and D mutually exclusive? Why or why not? select a letter for your answer

(A.) C and D are not mutually exclusive because P(C) + P(D) 1

(B.) C and D are mutually exclusive because they have different probabilities.

(C.) C and D are not mutually exclusive because P(C AND D) 0

(D.) There is not enough information to determine if C and D are mutually exclusive.

3.) Are C and D independent events? Why or why not? Select a letter for your answer

(A.) The events are not independent because P(C | D) P(C)

(B.)The events are independent because they are mutually exclusive.

(C.) The events are not independent because the sum of the events is less than 1.

(D.) The events are not independent because P(C) × P(D) P(C | D)

4.) Find P(D | C).

P ( C | D) = 0.6 = P (C and D) / P (D)

Thus,

P ( C and D ) = 0.6 * 0.5 = 0.30

For mutually exclusive events, occurence of one automatically cancels the possibility of the occurence of the other event.

Thus, so for mutually exclusive events, P ( C and D) = 0 which is not true.

So, option c is correct.

For independent events. P ( C and D ) = P (C) . P(D)

in our case:

P (C) . P(D) = 0.4 * 0.5 = 0.2 which is not equal to P(C and D)

so, the events are not independent.

Thus,

option A is correct.

P ( D | C) = P (C and D) / P (C)

= 0.3 / 0.4

= 0.75

Hope this helps.

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