Question

20
type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s)
lucas has five buttons in a container. each button is a different shape. there is a star, an oval, a hexagon, a circle, and a heart. he picks one
button, replaces it, and then picks another button.
the sample size for this compound event is
suppose one square - shaped button is added to the container. if lucas repeats the same picking process, then the sample size would be

Explanation:

Step1: <Determine initial number of buttons>

Initially, there are 5 buttons.

Step2: <Add one button>

After adding a square - shaped button, the number of buttons becomes \(n = 5+1=6\).

Step3: <Use compound - event sample - size formula>

For a compound event (picking a button, replacing it, and then picking another button), the sample size \(N\) is given by \(N=n\times n\) (since for each of the first pick (with \(n\) possibilities), there are \(n\) possibilities for the second pick). Substituting \(n = 6\), we get \(N=6\times6\).
$$N = 36$$

Answer:

36