Lemma
EasyConditional probability
OpenStax, Introductory Statistics 2e §3.2 Independent and Mutually Exclusive Events · Try It 5 · Probability · Conditional probability

Independent and Mutually Exclusive Events · Try It 5

Let event A = learning Spanish. Let event B = learning German. Then A AND B = learning Spanish and German. Suppose P(A) = 0.4 and P(B) = 0.2. P(A AND B) = 0.08. Are events A and B independent? Hint: You must show ONE of the following:

• P(A|B) = P(A)
• P(B|A) = P(B)
• P(A AND B) = P(A)P(B)

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OpenStax, Introductory Statistics 2e · §3.2 Independent and Mutually Exclusive Events · Try It 5

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