Question

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 \boxed{}. 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: Calculate initial sample size

Since there are 5 buttons, and each pick is independent (with replacement), the total number of possible outcomes is the product of the number of choices for each pick.
$5 \times 5 = 25$

Step2: Calculate new sample size

After adding 1 square button, there are 6 buttons total. Again, multiply the number of choices for each pick.
$6 \times 6 = 36$

Answer:

25
36