The students of a high school are 51% males. Of the students at this high school 45% of males and 40% of females said they regularly attend concerts.

Answer:

(b) Probability that a student is male and attends concert = 22.95%

(c) Probability that a student is female and does not attend concert = 29.4%

(d) Probability that a student attends concerts = 42.55%

Step-by-step explanation:

P.S - The exact question is -

Given - The population of a high school is 51% male. 45% of the males and 40% of the females attend concerts.

To find - (a) Make a tree diagram based on the information above.

               (b) Find the probability that a student is male and attends    

                    concerts.

               (c) Find the probability that a student is female and does not

                    attend concerts.

                (d) Find the probability that a student attends concerts.

Proof -

Let the total population of the high school = 100 x

Given that,

The students of a high school are 51% males

⇒Total males in the high school = 51% × 100 x

                                                      = [tex]\frac{51}{100}[/tex] × 100 x = 51 x

⇒Total males in the high school = 51 x

⇒Total females in the high school = 100 x - 51 x = 49 x

Now,

Given that,

Of the students at this high school 45% of males and 40% of females said they regularly attend concerts.

⇒Total number of males that attend the concert = 45% × 51 x

                                                                                = [tex]\frac{45}{100}[/tex] × 51 x  = 22.95 x

⇒Total number of males that attend the concert = 22.95 x

And

Total number of males that do not attend the concert = 51 x - 22.95 x

                                                                                          = 28.05 x

⇒Total number of males that do not attend the concert = 28.05 x

Also,

Total number of females that attend the concert = 40% × 49 x

                                                                                = [tex]\frac{40}{100}[/tex] × 49 x  = 19.6 x

⇒Total number of females that attend the concert = 19.6 x

And

Total number of females that do not attend the concert = 49 x - 19.6 x

                                                                                             = 29.4 x

⇒Total number of females that do not attend the concert = 29.4 x

(a)

The tree diagram is as follows :

(b)

Probability that a student is male and attends concert = [tex]\frac{22.95 x}{100 x}[/tex] × 100 %

                                                                                          = 22.95%

⇒Probability that a student is male and attends concert = 22.95%

(c)

Probability that a student is female and does not attend concert = [tex]\frac{29.4x}{100x}[/tex] × 100%

                                                                                                            = 29.4%

⇒Probability that a student is female and does not attend concert = 29.4%

(d)

Probability that a student attends concerts = [tex]\frac{22.95x + 19.6x}{100x}[/tex] ×100%

                                                                        = [tex]\frac{42.55}{100}[/tex] ×100%

                                                                        = 42.55%

⇒Probability that a student attends concerts = 42.55%

10
9
Ryan and Daniel are both packing boxes at a factory. Ryan can pack three boxes every hour. The number of boxes Daniel can pack in
x hours is represented by the equation below.
y = 45
Which of the following correctly describes the two functions?
OA. The number of boxes that can be packed by Ryan and Daniel each increases over time. Daniel's function has a greater rate of
change than Ryan's function indicating that Daniel can pack more boxes per hour.
0
ОВ.
The number of boxes that can be packed by Ryan and Daniel each decreases over time. Daniel's function has a greater rate of
change than Ryan's function, indicating that Daniel can pack fewer boxes per hour.
OC.
The number of boxes that can be packed by Ryan and Daniel each increases over time. Ryan's function has a greater rate of
change than Daniel's function, indicating that Ryan can pack more boxes per hour.
The number of boxes that can be packed by Ryan and Daniel each decreases over time. Ryan's function has a greater rate of
change than Daniel's function, indicating that Ryan can pack fewer boxes per hour.
OD.
10
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Submit
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