SOMEBODY PLEASE HELP ME WITH THE TWO WAY TABLES FOR GEOMETRY!! I NEED HELP VERY SOON PLEASE

Question

	Studied less than two hours(L)	Studied more than two hours(M)	total
Studied independantly (G)	12	4	16
Studied with a group(G)	8	11	19
total	20	15	35

   

a) What is the probability that a randomly chosen student studied less than two hours? P(L)

   b) What is the probability that a randomly chosen student studied independently for more than two hours? P (I and M)

   c) What is the probablity that a student who studied for more than two hours was studying in groups? P(G l M)

   d) What is the probability that a student studied independently, given they studied less than two hours? P(I l L)

   e) What is the probability that a student studied independently or studied more than two hours? P(I or M) 

Answer 1

a) What is the probability that a randomly chosen student studied less than two hours? P(L)

Probability = part/whole

Less than 2 hours = 12 + 8 = 20

Out of total students = 35

P(L) = 20/35 simplify by dividing by 5 = 4/7

   b) What is the probability that a randomly chosen student studied independently for more than two hours? P (I and M)

Must be at the intersection of the “studying independently” row and the “more than 2 hours” column = 4

out of total students = 35

P(I and M) =4/35

   c) What is the probablity that a student who studied for more than two hours was studying in groups? P(G l M)

We know that they studied more than 2 hours = given

—> this will be our whole (the denominator) because we are only taking from the total of people who studied more than 2 hours = 15

The numerator is going to be the number of people who studied in groups that are in the more than 2 hours column = 11

P(group given more than 2 hrs) = 11/15

   d) What is the probability that a student studied independently, given they studied less than two hours? P(I l L)

They studied less than 2 hours = given

—> this will be our denominator = 20

The numerator will be the number of people who studied independently that are in this less than 2 hours column= 12

P(independently given less than 2 hours) = 12/20 reduce by dividing by 4 = 3/5

   e) What is the probability that a student studied independently or studied more than two hours? P(I or M)

Or means add

*BUT you cannot double count the box where I and M intersect P(I and M) because you’d be counting the same group of people twice*

P(I or M) = P(I) + P(M) - P(I and M)

P(I or M) = (independent total + more than 2 hours total - intersection) / all divided by total people

P(independent) = total row = 16 people

P (more than 2 hours) = total column = 15 people

P(intersection of independent row and more than 2 hours column) = 4 people

Total people = 35

P(I or M) = (16 + 15 - 4) / 35

= 27/35

Answer 2

a) P(L) = 20/35 = 4/7 = about 57.14%

b) P(I&M) = 4/35 = about 11.43%

c) P(G/M) = 11/15 = about 73.33%

d) P(I/L) = 12/20 = 3/5 = 60%

d) P(I v M) = 27/35 = about 77.14%