Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.70 and P(B) = 0.30. If an amount is zero, enter "0". a. What is P(AB)? b. What is P(A/B)? c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Do you agree with this statement? Use the probability information in this problem to justify your answer. -Select your answer, because P(A/B)-Select your answer ✓ P(A).

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Assume that we have two events, \( A \) and \( B \), that are mutually exclusive. Assume further that we know \( P(A) = 0.70 \) and \( P(B) = 0.30 \).

If an amount is zero, enter “0”.

a. What is \( P(A \cap B) \)?

[Input box]

b. What is \( P(A|B) \)?

[Input box]

c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Do you agree with this statement? Use the probability information in this problem to justify your answer.

- [Dropdown] - because \( P(A|B) \) - [Dropdown] - \( P(A) \).

d. What general conclusion would you make about mutually exclusive and independent events given the results of this problem?

- [Dropdown]
Transcribed Image Text:Assume that we have two events, \( A \) and \( B \), that are mutually exclusive. Assume further that we know \( P(A) = 0.70 \) and \( P(B) = 0.30 \). If an amount is zero, enter “0”. a. What is \( P(A \cap B) \)? [Input box] b. What is \( P(A|B) \)? [Input box] c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Do you agree with this statement? Use the probability information in this problem to justify your answer. - [Dropdown] - because \( P(A|B) \) - [Dropdown] - \( P(A) \). d. What general conclusion would you make about mutually exclusive and independent events given the results of this problem? - [Dropdown]
Expert Solution
Step 1: Define the terms independent and mutually exclusive events.

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Independent events: 

Let A and B be any two events are said to be independent if,

Statistics homework question answer, step 1, image 1

Mutually exclusive events: 

The two events are said to be mutually exclusive events if,

Statistics homework question answer, step 1, image 2

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