A group of nine singers includes 6 altos and 3 sopranos. An instructor randomly selects one of the singers to sing the first part of a duet and a different singer to sing the second part of a duet. Use a sample space to determine whether randomly selecting an alto first and randomly selecting a soprano second are independent events.

P(alto first) ⋅ P(soprano second) =

P(alto first and soprano second) =

Explanation:

1. P(alto first) ⋅ P(soprano second)

2. P(alto first and soprano second)

The number of events or elements in the set of  "alto first and soprano second" is equal to the number of elements contained in the set of altos multiplied by the number of elements contained in the set of sopranos.

That is

The sample space for selecting two singers from the nine singers is:

Thus:

Therefore, by definition, since P(alto first) ⋅ P(soprano second) = P(alto first and soprano second), the events are independent.

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490

step-by-step explanation:

the options are kind of confusing. i can tell you what i see going on here when i look at the graph.

the class and exam medians are closely related, and it looks like the low outlier on the exam did pull the median lower. [tex][/tex]