Question

Five Years after 650 high school seniors graduated, 400 had a college degree and 310 were married. Half of the students with college degrees were married.
a.) What is the probability that a student has a college degree or married?
b.)what is the probability that a student has a college degree or is not married.
c.)What is the probility that a student does not have a college degree or is married

Answer 1

A) 78.4%
B) 83%
c) 69%

Answer 2

@hisham1 how ?

Answer 3

@hisham1: Please do not pass out answers. Instead, provide guidance so that Mhm120 can arrive at the correct results on his/her own. Refer to the Code of Conduct, please.

Answer 4

im sorry, my laptop just died!

Answer 5

@mathmale could you please explain to me how to do this problem?

Answer 6

anyways, you begin with the total, which is 650 students, and that will be your denominator for the whole time.

Answer 7

alright noted what's next

Answer 8

While it's not strictly necessary, you (mhm120) might want to make what's called a "contingency table." The contents of this table come from the verbal problem statement.

Answer 9

Are you familiar with that name, "contingency table"?

Answer 10

400 had a college degree, 310 were married, and 200 were both married and had a college degree.

Answer 11

yes.

Answer 12

Would you (hisham1) mind drawing a contingency table and then demonstrating how to use it to answer these 3 questions? Remember, you're addressing mhm120, not me.

Answer 13

I am not familiar with what a contingency table is...

Answer 14

can you please excuse me, i have to go.

Answer 15

it's fine Can some please help me with the probelm cause I want to make sur eI understand the concepts

Answer 16

Any given person chosen at random from these 650 graduates could be
1) married,
2) unmarried,
3) a college graduate, or
4) not a college graduate.

Answer 17

We'll arrange this data in a table:

Coll Not coll
grad grad Totals
Married
Not mar
Totals 650

Answer 18

Referring to this table and to the original problem statement, could you fill in the table?

Answer 19

yes I could

Answer 20

Great. copy my table and paste it into your entry space, then fill it out.

Answer 21

Five Years after 650 high school seniors graduated, 400 had a college degree and 310 were married. Half of the students with college degrees were married.
a.) What is the probability that a student has a college degree or married?
b.)what is the probability that a student has a college degree or is not married.
c.)What is the probility that a student does not have a college degree or is married

Coll Not coll
grad grad Totals
Married
Not mar
Totals 650

Answer 22

just kidding i can't

Answer 23

We're told that 400 of the HS grads had a college degree, so we'll insert that sum, 400, at the bottom of the College degree column. Can you figure out what to do with the total numb er who were married?

Coll Not coll
grad grad Totals
Married
Not mar
Totals 400 650

Answer 24

200?

Answer 25

since it said half the students with a college degree were married.

Answer 26

Coll Not coll
grad grad Totals
Married 200
Not mar
Totals 400 650

True. What total number of students were married? Where do you put that info?

Answer 27

right under totals (the second row) and it would be 310

Answer 28

Coll Not coll
grad grad Totals
Married 200 310
Not mar
Totals 400 650

Right. of those 310 total who were married, how many were not college grads?

Answer 29

it would be half of 310? so 155?

Answer 30

The reasoning ("half") is correct, but that's not what the problem statement says, is it? A total of 310 were married, and 200 of those 310 were college grads. Therefore, the number of married peoople who did not have4 college degrees was what? (Subtract)

Answer 31

110

Answer 32

Agreed. Are you able to put that 110 into the table yourself? (Copy and paste.)

Answer 33

I would but when I copy and paste it it won't work properly it just glitches( I need to get my computer fixed)

Answer 34

But it goes not coll grad

Answer 35

Coll Not coll
grad grad Totals
Married 200 110 310
Not mar
Totals 400 650

How many students, total, are not college grads?

Answer 36

(Obtain this info from the table, immediately above

Answer 37

Hint: Subtract again!

Answer 38

If there are a total of 650 people here, and 400 of them are college grads, how many are not college grads?

Answer 39

wait what are we looking for now?

Answer 40

Number of peopole who are NOT college gradds.

Answer 41

oh ok sorry

Answer 42

Total 650
coll grads -400
------
Not col. grads:

Answer 43

250

Answer 44

Correct.

Coll Not coll
grad grad Totals
Married 200 110 310
Not mar
Totals 400 250 650

How many people,total, are not married?
How many people, total are neither married nor college grads?

Answer 45

200 & 140

Answer 46

For "not married", subtract 310 from 650.

Answer 47

340

Answer 48

Good! How many people, total are neither married nor college grads?

Answer 49

Coll Not coll
grad grad Totals
Married 200 110 310
Not mar 340
Totals 400 650

Answer 50

40

Answer 51

*140

Answer 52

This process goes much faster after you've done it a few times. Thanks for your patience. Yes, 140.

Answer 53

Coll Not coll
grad grad Totals
Married 200 110 310
Not mar 140 340
Totals 400 650

Answer 54

Can you now fill in the 2 missing numbers?

Answer 55

no it's fine.. I actually have a test tomorrow and so I wanted to really learn this. It's VERY helpful. (: and so the total Not coll frad would be 250 and not married college grads were 200

Answer 56

Coll Not coll
grad grad Totals
Married 200 110 310
Not mar 140 340
Totals 400 250 650

Answer 57

Coll Not coll
grad grad Totals
Married 200 110 310
Not mar 200 140 340
Totals 400 250 650

Answer 58

Yay!

Answer 59

Now we have 3 probabilities to find. The first one :
What is the probability that a student has a college degree or married?

Answer 60

is it \[\frac{ college degree/married }{ Total }\]

Answer 61

It's possible for a person to be both married and a college grad, right?
In this case, we're calculating what's called "joint probability" and then the probability of a "union." are you familiar with either term?

Answer 62

that wa s a guess though.. and ahah yes it is possible

Answer 63

an dim familiar with those but not super sure on what they are.

Answer 64

Let me type out the rule; we can discuss it later as needed.
P(A) or P(B)=

Answer 65

ok

Answer 66

Let me type out the rule; we can discuss it later as needed.
P(A or B) = P(A)+P(B) - P(A AND B).

Answer 67

This applies when there can be overlap of events A and B.
This applies when a person can be both married and have a college degree, right?

Answer 68

right.

Answer 69

So: Let Event A be "The person is married."
Let Event B be "The person is a college grad."

We need to find P(A), P(B) and P(A AND B).

How many people, total, are married?

Answer 70

total married is 310

Answer 71

Yes, 310 out of 650, so, P(A) is 310/650.
Now, how many peoopl ehave a college degree?

Answer 72

400

Answer 73

Right, and so P(B) is 400/650.
Now, how many peoople are both married and have a college degree?

Answer 74

Just look under the "college degree" column, immediately to the right of the "married" row.

Answer 75

200

Answer 76

Right, and so the joint probability of A and B is 200/650.

Following the formula I gave you earlier,
P(A or B) = P(A)+P(B) - P(A AND B).

Just stick in the values we found for P(A), P(B) and P(A and B).

It's very important that you be able to do this yourself.

The answer will look like

400+310-200
------------ P( married OR college grad)
650

Can you see where I got that?

Answer 77

Vaguely.. Sorry

Answer 78

Please go back and find our values for P(A) and P(B). type out those values below.

Answer 79

P(A) =310/650
P(B)=400/650
P(A&B)=200/650

Answer 80

So, if you add the first two together, you get (310+400)/650, or 710/650; if you then subtract 200/650, you get 510/650,

which is the same thing as I typed earlier:

400+310-200
------------ P( married OR college grad)
650

Answer 81

Divide 650 into 510; the resulting decimal fraction is the probability wanted in the first problem

Answer 82

mhm120: I'm afraid I must get off the 'Net soon. I'df like to encourage you to try solving the 2nd and 3rd problems in the same way. I'll probabl;y be on the Internet later today, so if you post anything, I'll likely see it and answer it. Great working with you.

Answer 83

is it 1.27?

Answer 84

Mind saying what state you're from and what grade (or college level) you're in?

Answer 85

510/650 would be a fraction LESS than 1, wouldn't it?

Answer 86

CA, 10th

Answer 87

why? aha

Answer 88

I'm in Kern County, CA, 3 hours north of LA. Pure curiosity.

Answer 89

ahhhh haha

Answer 90

are you a teacher?

Answer 91

Again, great talking with you. Hope we link up later today. Yes, I'm a retired college professor.

Answer 92

Thanks for your perseverance! Bye for now.

Answer 93

bye!

Answer 94

@mathmale oj I still need guidance for the last parts of this problem .

Answer 95

Coll Not coll
grad grad Totals
Married 200 110 310
Not mar 200 140 340
Totals 400 250 650

b.)what is the probability that a student has a college degree or is not married.

@Mhm120 : this problem may be done in the same way as the previous one.

How many of these people have college degrees?

Answer 96

250

Answer 97

Look at the sum at the bottom of the college grad column. What is it?