Answer:
[tex]P(Jazz\ and\ Jazz) = \frac{289}{14884}[/tex]
Step-by-step explanation:
Given
[tex]Classical = 42[/tex]
[tex]Pop = 25[/tex]
[tex]Jazz = 17[/tex]
[tex]Rock = 38[/tex]
Required
Determine the probability of selecting Jazz, twice
This probability can be represented using P(Jazz and Jazz) and is calculated as thus:
[tex]P(Jazz\ and\ Jazz) = P(Jazz) *P(Jazz)[/tex]
[tex]P(Jazz\ and\ Jazz) = \frac{n(Jazz)}{Total} * \frac{n(Jazz)}{Total}[/tex]
[tex]P(Jazz\ and\ Jazz) = \frac{17}{42 + 25 + 17 + 38} * \frac{17}{42 + 25 + 17 + 38}[/tex]
[tex]P(Jazz\ and\ Jazz) = \frac{17}{122} * \frac{17}{122}[/tex]
[tex]P(Jazz\ and\ Jazz) = \frac{17^2}{122^2}[/tex]
[tex]P(Jazz\ and\ Jazz) = \frac{289}{14884}[/tex]
