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.

the monthly balance will be $75,000

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

ask for details followreport by buttfacelily 2 minutes ago

answers

rauschg

rauschg · hand

know the answer? add it here!

step-by-step explanation: