1. There are 65 adults and 15 children in a movie theater. Of these people, 41 adults and 6 children bought popcorn.

a) What is the probability that a randomly selected person in the theater is a child or someone who bought popcorn.

b) What is the probability that a randomly selected person is an adult or someone who did not buy popcorn.

My answers are 0.70 and 0.925 respectively. My friends believe otherwise.

a) 0.70

b) 0.925

You are right and your friends are wrong.

Step-by-step explanation:

- 65 adults and 15 children in a movie theater

- 41 adults and 6 children bought popcorn

Number of children in the theatre = 15

Number of adults in the theatre = 65

Number of children that bought popcorn = 6

Number of children that did not buy popcorn = 15 - 6 = 9

Number of adults that bought popcorn = 41

Number of adults that did not buy popcorn = 65 - 41 = 24

Total number of persons that bought popcorn = 41 + 6 = 47

Number of people that did not buy popcorn = 80 - 47 = 33

Total number of persons in the theatre = 65 + 15 = 80

a) The probability that a randomly selected person in the theater is a child or someone who bought popcorn.

Required probability

= (number of children or people that bought popcorn) ÷ (total number of people)

There 15 children, and 47 people that bought popcorn, but of the 47, there are still 6 children amongst them.

Hence, the number of children or people that bought popcorn = 15 + 47 - 6 = 56

Total number of people = 80

Required probability = (56/80) = 0.70

b) The probability that a randomly selected person is an adult or someone who did not buy popcorn.

Required probability

= (number of adults or people who did not buy popcorn) ÷ (total number of people)

There are 65 adults, and 33 people that did not buy popcorn, but of the 33, there are still 24 adults amongst them.

Hence, the number of adults or people who did not buy popcorn

= 65 + 33 - 24 = 74

Total number of people = 80

Required probability = (74/80) = 0.925

You are right and your friends are wrong.

Hope this Helps!!!

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)