Venn Diagrams and Conditional Probability starter I. In a group of 16 atudents, 12 take art and 8 take musio. One student takes neither art nor musie. (a) Draw a Venn diagram to help you find the number of students who take both art and music.

A number is selected at ramdom from the single digit matwral number. The probabilify- of that number being even- is \( \frac{1}{2} \) False.

Determina si las siguientes situaciones son eventos dependientes: sacar una bola roja de una caja, no regresarla y luego sacar otra bola.

The chance of winning a particular lottery game is 1 in 32000, How many tickets would I need to buy in order to improve the chance to 1 in 3200 ? If a machine produces 40 items in 5 minutes, how many liems would it produce in a day?

Find c.df \( f(x) \) and \( P\left(\frac{1}{3}<x<\frac{1}{3}\right) \) of the Eollowing \[ \begin{aligned} f(x)=12 x^{2}(1-x) & \text { For } 0<x<1 \\ =0 & \text { otherwise }\end{aligned} \]

A fair coin tossed 10 times find the propablity getting atmost six head. If \( x \sim B(n p) \) and \( E(x)=6 \quad \operatorname{var}(x) \) find \( n 4 p \)