Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Ask your questions and receive precise answers from experienced professionals across different disciplines. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Which statement implies that A and B are independent events?

Sagot :

pepe11
A and B are insdependent if prob (A and B) = prob(A) x prob(B) 

Answer with explanation

Two events A and B are said to be Independent ,if occurrence of one of them does not affect the occurrence of other.

For, example: A die is thrown once.Find the Probability of getting multiple of,2 and Probability of getting multiple of 3. Check whether these two events are Independent or not.

Probability of getting multiple of 2, when a die is thrown once ={2,4,6}

   [tex]=\frac{3}{6}\\\\=\frac{1}{2}[/tex]

Probability of getting multiple of 3, when a die is thrown once ={3,6}

      [tex]=\frac{2}{6}\\\\=\frac{1}{3}[/tex]  

[tex]A\cap B={6}\\\\ P(A \cap B)=\frac{1}{6}\\\\P(A) \times P(B) =\frac{1}{2}\times\frac{1}{3}\\\\=\frac{1}{6}\\\\=P(A\cap B)[/tex]

So, if [tex]P(A \cap B)=P(A) \times P(B)[/tex]

Then ,events A and B are Independent events.

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.