anonymous
  • anonymous
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.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
So there are 18 total utensils in the box. What's the probability that a fork is drawn first?
anonymous
  • anonymous
12 over 18?
anonymous
  • anonymous
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?

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anonymous
  • anonymous
6 over 17
anonymous
  • anonymous
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?
anonymous
  • anonymous
Do i cross multiply or go straight across?
anonymous
  • anonymous
To multiply fractions, multiply the numerators together and multiply denominators together
anonymous
  • anonymous
12 over 14 ?
anonymous
  • anonymous
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.
anonymous
  • anonymous
OH, duh for me, 12/21. Sorry :p
anonymous
  • anonymous
Nope. Try again. Use a calculator.
anonymous
  • anonymous
I think
anonymous
  • anonymous
What's 3 x 17 ?
anonymous
  • anonymous
Wait i thought we were timing 7 times 3?
anonymous
  • anonymous
Where does the 7 come from? The denominator is 3 x 17
anonymous
  • anonymous
i AM SO SORRY. Rough morning. okay so 17 times 3 is 51 so its 12/51?
anonymous
  • anonymous
Very good. But this can be reduced. 3 is a common factor, so divide both numerator and denominator by 3. What do you get?
anonymous
  • anonymous
4/17?
anonymous
  • anonymous
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?
anonymous
  • anonymous
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)
anonymous
  • anonymous
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?
anonymous
  • anonymous
Yes, but i thought it would just switch the fractions that we multiplied around and i would get the same answer
anonymous
  • anonymous
Maybe, but let's go through it.
anonymous
  • anonymous
So, what's the probability of choosing a knife out of the box first?
anonymous
  • anonymous
6/17
anonymous
  • anonymous
Remember, when you begin, there are 18 utensils in the box. Try again.
anonymous
  • anonymous
6/18 which simplifies to 1/3
anonymous
  • anonymous
Exactly. Now, there are 17 utensils in the box. What's the probability of choosing a fork second?
anonymous
  • anonymous
12/17
anonymous
  • anonymous
Correct. Now, the probability of choosing knife then fork is the product of these two probabilities. What do you get?
anonymous
  • anonymous
12/51
anonymous
  • anonymous
Excellent. Now, 3 is also a common factor so this fraction can be reduced, to what?
anonymous
  • anonymous
6/17
anonymous
  • anonymous
Not quite. What's 12 divided by 3?
anonymous
  • anonymous
oh, 4 sorry
anonymous
  • anonymous
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.
anonymous
  • anonymous
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?
anonymous
  • anonymous
So I got 8/34 but i feel like thats wrong
anonymous
  • anonymous
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,\[\frac{ 1 }{ 5 } + \frac{ 3 }{ 5 } = \frac{ 4 }{ 5 }\]
anonymous
  • anonymous
2/6 which simplifies to 1/3???
anonymous
  • anonymous
Nope. I'll write it out.\[\frac{ 4 }{ 17 } + \frac{ 4 }{ 17 } = ??\]
anonymous
  • anonymous
Keep the denominator the same and add the numerators.
anonymous
  • anonymous
8/17
anonymous
  • anonymous
Bingo! That's your answer. Good job.
anonymous
  • anonymous
Thank you
anonymous
  • anonymous
You're welcome.

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