type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction…

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 .

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 .

Answer

Explanation:

Step1: Calculate initial sample - size

Since there are 5 buttons and the picking is with replacement (two - step process), we use the multiplication principle. The number of possible outcomes for the first pick is 5, and for the second pick is also 5. So the sample size $n_1=5\times5 = 25$.

Step2: Calculate new sample - size

When one more button is added, there are 6 buttons. Using the multiplication principle again for the two - step picking process with replacement, the number of possible outcomes for the first pick is 6, and for the second pick is also 6. So the sample size $n_2=6\times6=36$.

Answer:

25 36