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.

1. anonymous

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

2. anonymous

12 over 18?

3. 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?

4. anonymous

6 over 17

5. 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?

6. anonymous

Do i cross multiply or go straight across?

7. anonymous

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

8. anonymous

12 over 14 ?

9. 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.

10. anonymous

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

11. anonymous

Nope. Try again. Use a calculator.

12. anonymous

I think

13. anonymous

What's 3 x 17 ?

14. anonymous

Wait i thought we were timing 7 times 3?

15. anonymous

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

16. anonymous

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

17. 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?

18. anonymous

4/17?

19. 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?

20. 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)

21. 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?

22. anonymous

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

23. anonymous

Maybe, but let's go through it.

24. anonymous

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

25. anonymous

6/17

26. anonymous

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

27. anonymous

6/18 which simplifies to 1/3

28. anonymous

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

29. anonymous

12/17

30. anonymous

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

31. anonymous

12/51

32. anonymous

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

33. anonymous

6/17

34. anonymous

Not quite. What's 12 divided by 3?

35. anonymous

oh, 4 sorry

36. 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.

37. 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?

38. anonymous

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

39. 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,$\frac{ 1 }{ 5 } + \frac{ 3 }{ 5 } = \frac{ 4 }{ 5 }$

40. anonymous

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

41. anonymous

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

42. anonymous

Keep the denominator the same and add the numerators.

43. anonymous

8/17

44. anonymous

45. anonymous

Thank you

46. anonymous

You're welcome.

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