the probability for event a is 0.4, the probability for event b is 0.2, and the probability of events a and b is 0.1.
why are the events not independent?

- the sum of p(a) and p(b) is greater than p(a and b)
- the product of p(a) and p(b) is greater than p(a and b)
- the product of p(a) and p(b) is not equal to p(a and b)
- the sum of p(a) and p(b) is not equal to p(a and b)

Question

the probability for event a is 0.4, the probability for event b is 0.2, and the probability of events a and b is 0.1.
why are the events not independent?

- the sum of p(a) and p(b) is greater than p(a and b)
- the product of p(a) and p(b) is greater than p(a and b)
- the product of p(a) and p(b) is not equal to p(a and b)
- the sum of p(a) and p(b) is not equal to p(a and b)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Independent Events" ], "new_concepts": [], "current_concepts": [ "Independent Events", "Probability Multiplication Rule" ] } ## State the given values Using the *Independent Events* knowledge point $$ \begin{aligned} P(A) &= 0.4 \ P(B) &= 0.2 \ P(A \text{ and } B) &= 0.1 \end{aligned} $$ ## Apply the test for independence Using the *Independent Events* knowledge point $$ \begin{aligned} P(A) \times P(B) &= 0.4 \times 0.2 = 0.08 \ P(A \text{ and } B) &= 0.1 \ P(A) \times P(B) & eq P(A \text{ and } B) \quad (0.08 eq 0.1) \end{aligned} $$

The sum of P(A) and P(B) is greater than P(A and B)

The product of P(A) and P(B) is greater than P(A and B)

The product of P(A) and P(B) is not equal to P(A and B)

The sum of P(A) and P(B) is not equal to P(A and B)

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Independent Events" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

State the given values

Apply the test for independence

Answer: