Independent and Mutually Exclusive Events · Try It 5

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

• $P(A|B)=P\left(A\right)$
• $P(B|A)=P\left(B\right)$
• $P\left(A\cap B\right)=P\left(A\right)P\left(B\right)$

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