Question

A box contains 12 plastic forks and 6 plastic knives. If two utensils are chosen at random from the box without replacement, what is the probability that they are different?

A)
13
17
B)
4
17
C)
8
17
D)
9
17
PLEASEE EXPLAIN HOW TO DO THIS. I don't just want the answer :) Thank you VERY much.

Answer 1

So there are 18 total utensils in the box. What's the probability that a fork is drawn first?

Answer 2

12 over 18?

Answer 3

Correct. It can be reduced to 2/3. The fork is NOT replaced so there are now 17 utensils in the box. What's the probability that a knife is chosen next?

Answer 4

6 over 17

Answer 5

Very good. So the probability that a fork is drawn first and a knife is drawn second is the product of these two individual probabilities, i.e. 2/3 x 6/17. What do you get?

Answer 6

Do i cross multiply or go straight across?

Answer 7

To multiply fractions, multiply the numerators together and multiply denominators together

Answer 8

12 over 14 ?

Answer 9

Not quite.\[\frac{ 2 }{ 3 } \times \frac{ 6 }{ 17 } = \frac{ 2 \times 6 }{ 3 \times 17 } = ?\]And don't forget to reduce the answer to lowest terms.

Answer 10

OH, duh for me, 12/21. Sorry :p

Answer 11

Nope. Try again. Use a calculator.

Answer 12

I think

Answer 13

What's 3 x 17 ?

Answer 14

Wait i thought we were timing 7 times 3?

Answer 15

Where does the 7 come from? The denominator is 3 x 17

Answer 16

i AM SO SORRY. Rough morning. okay so 17 times 3 is 51 so its 12/51?

Answer 17

Very good. But this can be reduced. 3 is a common factor, so divide both numerator and denominator by 3. What do you get?

Answer 18

4/17?

Answer 19

Excellent. So the probability of choosing a fork first and then a knife is 4/17. But we're not done yet. Do you know why?

Answer 20

Ummm, well I dont think it can be simplified further... So i'm not really sure. Because it wants to know the probability that they are different??(Again sorry, rough morning an im horrible at math)

Answer 21

No problem. You're right that it can't be simplified further. But, there is another possibility that satisfies the question. The question asks for the probability that the two choices will be different, and you calculated the probability of choosing a fork, then a knife. But what about choosing a knife first, then a fork. You also need to calculate that probability. Understand?

Answer 22

Yes, but i thought it would just switch the fractions that we multiplied around and i would get the same answer

Answer 23

Maybe, but let's go through it.

Answer 24

So, what's the probability of choosing a knife out of the box first?

Answer 25

6/17

Answer 26

Remember, when you begin, there are 18 utensils in the box. Try again.

Answer 27

6/18 which simplifies to 1/3

Answer 28

Exactly. Now, there are 17 utensils in the box. What's the probability of choosing a fork second?

Answer 29

12/17

Answer 30

Correct. Now, the probability of choosing knife then fork is the product of these two probabilities. What do you get?

Answer 31

12/51

Answer 32

Excellent. Now, 3 is also a common factor so this fraction can be reduced, to what?

Answer 33

6/17

Answer 34

Not quite. What's 12 divided by 3?

Answer 35

oh, 4 sorry

Answer 36

Right. So now you have everything you need. Notice that the probabilities for the two possibilities ended up the same but the individual fractions were not simply reversed. So you can't assume things, you must go through and do the calculations.

Answer 37

Alright, now to answer the question. You've determined that the probability of choosing a fork first and a knife second is 4/17. AND, you've determined that the probability of choosing a knife first and a fork second is 4/17. Thses are the only two scenarios that satisfy the question. So the final answer is the SUM of these two probabilities. What is it?

Answer 38

So I got 8/34 but i feel like thats wrong

Answer 39

Sorry. That's not it. Remember, we're not multiplying fractions here, we're adding them. When adding fractions with a common denominator, keep the denominator the same and add the numerators. For example,\[\frac{ 1 }{ 5 } + \frac{ 3 }{ 5 } = \frac{ 4 }{ 5 }\]

Answer 40

2/6 which simplifies to 1/3???

Answer 41

Nope. I'll write it out.\[\frac{ 4 }{ 17 } + \frac{ 4 }{ 17 } = ??\]

Answer 42

Keep the denominator the same and add the numerators.

Answer 43

8/17

Answer 44

Bingo! That's your answer. Good job.

Answer 45

Thank you

Answer 46

You're welcome.