SOLUTION: Grade Female Male 9th Female 4 Male 6 10th Female 5 Male 5 11th Female 4 Male 6 12th Female 8 Male 2 The Washington High School student Council has 40 r

Algebra ->  Probability-and-statistics -> SOLUTION: Grade Female Male 9th Female 4 Male 6 10th Female 5 Male 5 11th Female 4 Male 6 12th Female 8 Male 2 The Washington High School student Council has 40 r      Log On


   

Question 241974: Grade Female Male
9th Female 4 Male 6
10th Female 5 Male 5
11th Female 4 Male 6
12th Female 8 Male 2
The Washington High School student Council has 40 representatives by grade and gender. One student council representative will be chosen at random to give a tour to a visitor. What is the probability that the representative will be either a female or in the 10th grade?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you need to create an array with totals.

that would look like this: 



grade       female       male       total
9th           4           6           10
10th          5           5           10
11th          4           6           10
12th          8           2           10

total        21          19           40


total of 40 students.
total of 10 in each grade
total of 21 females
total of 19 males

probability that the representative will be a female is 21 / 40

probability that the representative will be from the 10th grade is 10 / 40

probability that the representative will be either a female OR from the 10th grade is NOT 21 + 10 = 31/40

this is because the females from the 10th grade will be double counted because they are females AND in the 10th grade.

you have to subtract the females in the 10th grade to get a total of:

(21 + 10 - 5) / 40 = (31-5)/40 = 26/40

This avoids them being double counted if they are both females and in the 10th grade.

to see how that works, try simpler numbers.

let there be 3 females and 1 male in the 10th grade.

let there be 3 females and 3 males in the 11th grade.

you have a total of 10 students.
4 in the 10th grade
6 in the 11th grade
6 females
4 males
you want to pick one representative.

probability that person will be a female OR in the 10th grade is:

probability of being in the 10th grade is 4 out of 10
probability of being a female is 6 out of 10

probability of being a female OR in the 10th grade is NOT (4+6)/10 = 10/10 because 3 females are being double counted.

subtract 3 females from 10 and you get 7 out of 10.

probability of being female OR in the 10th grade is 7 out of 10.

there are 10 possible choices for representatives.

we could get:
f10 (means female in the 10th grade)
f10
f10
m10 (means male in the 10th grade)
f11 (means female in the 11th grade)
f11
f11
m11 (means male in the 11th grade)
m11
m11

the 4 possibilities from the 10th grade are:

f10 f10 f10 m10

the 6 possibilities from the females are:

f10 f10 f10 f11 f11 f11

females in the 10th grade are counted twice.

subtract females in the 10th grade and you get

m10 f10 f10 f10 f11 f11 f11 which totals 7 out of 10

the general equation is:

probability of (A OR B) equals probability of (A) PLUS probability of (B) MINUS probability of (A AND B)

Since A AND B are in both A and B, you have to subtract them so they don't get double counted.