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anonymous
 one year ago
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.
anonymous
 one year ago
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.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So there are 18 total utensils in the box. What's the probability that a fork is drawn first?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Correct. 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?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Very 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
 one year ago
Best ResponseYou've already chosen the best response.0Do i cross multiply or go straight across?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0To multiply fractions, multiply the numerators together and multiply denominators together

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Not 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
 one year ago
Best ResponseYou've already chosen the best response.0OH, duh for me, 12/21. Sorry :p

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Nope. Try again. Use a calculator.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait i thought we were timing 7 times 3?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Where does the 7 come from? The denominator is 3 x 17

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i AM SO SORRY. Rough morning. okay so 17 times 3 is 51 so its 12/51?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Very good. But this can be reduced. 3 is a common factor, so divide both numerator and denominator by 3. What do you get?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Excellent. 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
 one year ago
Best ResponseYou've already chosen the best response.0Ummm, 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
 one year ago
Best ResponseYou've already chosen the best response.0No 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
 one year ago
Best ResponseYou've already chosen the best response.0Yes, but i thought it would just switch the fractions that we multiplied around and i would get the same answer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Maybe, but let's go through it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So, what's the probability of choosing a knife out of the box first?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Remember, when you begin, there are 18 utensils in the box. Try again.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.06/18 which simplifies to 1/3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Exactly. Now, there are 17 utensils in the box. What's the probability of choosing a fork second?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Correct. Now, the probability of choosing knife then fork is the product of these two probabilities. What do you get?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Excellent. Now, 3 is also a common factor so this fraction can be reduced, to what?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Not quite. What's 12 divided by 3?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Right. 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
 one year ago
Best ResponseYou've already chosen the best response.0Alright, 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
 one year ago
Best ResponseYou've already chosen the best response.0So I got 8/34 but i feel like thats wrong

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry. 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
 one year ago
Best ResponseYou've already chosen the best response.02/6 which simplifies to 1/3???

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Nope. I'll write it out.\[\frac{ 4 }{ 17 } + \frac{ 4 }{ 17 } = ??\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Keep the denominator the same and add the numerators.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Bingo! That's your answer. Good job.
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