Probability...Help

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GWS

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I came accross a new question that has four parts. I don't know what to do with parts b through d. I think I got part a down. Can you let me know?

Rita bought two dozen superballs to give out at her birthday party, and she put them in a bag. A third of the superballs were blue, 25% were striped, and eighth were hot pink, and the rest were made to glow in the dark.

a. Janet arrived first, and Rita asked him to reach into the bag without looking and take a ball. What is the probability that Janet's ball will glow in the dark?

Is the answer 7/24?


b. Janet picked a blue ball. Jack arrived next and said she hoped to pick hot pink. What is the probability she will get her wish?


c. Jack didn't get what she'd wanted, but Peter, who picked next, did get hot pink. What was tthe probability of this happening?

d. Peter traded with Jack for her striped superball. Larry picked next, hoping for a glow-in-the dark ball. What is the probability of her choosing one?

I am so lost. What are the answers to these tough questions?
 
a) Please proof the exercise. Are "eight" hot pink, or are "one-eighth"? Also, should we assume that the identifiers are unique? For instance, should we assume that striped balls don't glow in the dark, and that glowing balls aren't hot pink?

Thank you.

b) After a "blue" is removed, how many balls remain? How many are "hot pink"? So what is the probability of picking a "hot pink"?

c) If Ms. Jack didn't get a "hot pink", then she got something else. How many balls remained? How many were "hot pink"? So what were the odds that the next person would draw a "hot pink"?

(I'm not going to ask why a girl is going by the name "Jack". Maybe it's short for "Jackie"....)

d) The trading is irrelevant, as it does not affect what remains inside the bag. You now know that Ms. Jack got a "striped". In particular, you know she did not get a "glows in the dark". So how many balls remain? How many of them are "glows"?

(The girl's name is "Larry"...?)

Eliz.
 
GWS said:
I came accross a new question that has four parts. I don't know what to do with parts b through d. I think I got part a down. Can you let me know?

Rita bought two dozen superballs to give out at her birthday party, and she put them in a bag. A third of the superballs were blue, 25% were striped, and one-eighth were hot pink, and the rest were made to glow in the dark.

a. Janet arrived first, and Rita asked her to reach into the bag without looking and take a ball. What is the probability that Janet's ball will glow in the dark?

Is the answer 7/24?


b. Janet picked a blue ball. Jack arrived next and said he hoped to pick hot pink. What is the probability he will get his wish?


c. Jack didn't get what he'd wanted, but Peter, who picked next, did get hot pink. What was the probability of this happening?

d. Peter traded with Jack for his striped superball. Larry picked next, hoping for a glow-in-the dark ball. What is the probability of his choosing one?

I am so lost. What are the answers to these tough questions?
Click to expand...
 
My Reply To Stapel...GWS

Here is the correct math question and choices.


Rita bought two dozen superballs to give out at her birthday party, and she put them in a bag. A third of the superballs were blue, 25% were striped, and one-eighth were hot pink, and the rest were made to glow in the dark.

a. Janet arrived first, and Rita asked her to reach into the bag without looking and take a ball. What is the probability that Janet's ball will glow in the dark?

Well, 1/3 of 24 balls = 8; 1/4 of 24 balls = 6; 1/8 of 24 balls = 3. I added 8 + 6 + 3 to get 17 balls. To get the rest I subtracted 17 from 24 balls and got 7. So, my answer to part a = 7/24. Is this correct?


b. Janet picked a blue ball. Jack arrived next and said he hoped to pick hot pink. What is the probability he will get his wish?

Here I got lost. If Janet picked a blue ball, then there 23 balls left, right? Okay, 3 balls are hot pink. Is the answer 3/23?


c. Jack didn't get what he'd wanted, but Peter, who picked next, did get hot pink. What was the probability of this happening?

I don't know the logic behind this next question. Can you help me?

d. Peter traded with Jack for his striped superball. Larry picked next, hoping for a glow-in-the dark ball. What is the probability of his choosing one?

There are 7 glow in the dark balls. I stated the answer to be 6/23. Is this correct?
Can you help me with the answers?
 
Thank you for posting corrections. :D

a) I agree with your reasoning and solution.

b) I agree with your reasoning and solution.

(If you're getting "lost", make a table. Make five columns, headed respectively with "blue", "striped", "pink", "glow", and "total". In the first row, enter "8", "6", "3", "7", and "24". In the second row, put "Janet" in the "blue" column. In the third row, put your new set-up: "7", "6", "3", "7", and "23". From this, you can read off the answer to (b): there are three "pink" balls out of twenty-three "total", so Jack has a 3-in-23 chance of drawing "pink".)

c) By looking ahead to (d), we know that Jack actually drew a "striped" in (b), so put "Jack" in the "striped" column for the fourth row. The fifth row then has your new totals: "7", "5", "3", "7", and "22". Read off your answer.

d) If there were twenty-three balls back in (b), before Jack drew, then can there still be twenty-three balls when Larry draws?

Continue the table I explained above. You'll be able to "see" the answer directly.

Eliz.
 
Re: My Reply To Stapel...GWS

GWS said:
Rita bought two dozen superballs to give out at her birthday party, and she put them in a bag. A third of the superballs were blue, 25% were striped, and one-eighth were hot pink, and the rest were made to glow in the dark.

a. Janet arrived first, and Rita asked her to reach into the bag without looking and take a ball. What is the probability that Janet's ball will glow in the dark?

Well, 1/3 of 24 balls = 8; 1/4 of 24 balls = 6; 1/8 of 24 balls = 3. I added 8 + 6 + 3 to get 17 balls. To get the rest I subtracted 17 from 24 balls and got 7. So, my answer to part a = 7/24. Is this correct?

YES! Good job.

b. Janet picked a blue ball. Jack arrived next and said he hoped to pick hot pink. What is the probability he will get his wish?

Here I got lost. If Janet picked a blue ball, then there 23 balls left, right? Okay, 3 balls are hot pink. Is the answer 3/23?

YES! Good job.

c. Jack didn't get what he'd wanted, but Peter, who picked next, did get hot pink. What was the probability of this happening?

I don't know the logic behind this next question. Can you help me?

There's now 22 balls left (after Jack's pick); ok?
And the 3 hotpinks are still left; ok?

d. Peter traded with Jack for his striped superball. Larry picked next, hoping for a glow-in-the dark ball. What is the probability of his choosing one?

There are 7 glow in the dark balls. I stated the answer to be 6/23. Is this correct? : NO!

Yes, there are still 7 glowers left: we know Jack didn't pick one; he got a striped;
But there are now 21 balls left: 3 have been picked by Janet, Jack and Peter.
OK?
Click to expand...
 
Stapel...My Reply

You stated:

c) By looking ahead to (d), we know that Jack actually drew a "striped" in (b), so put "Jack" in the "striped" column for the fourth row. The fifth row then has your new totals: "7", "5", "3", "7", and "22". Read off your answer.

I say the answer to part c = 3/22. Is this correct?d) If there were twenty-three balls back in (b), before Jack drew, then can there still be twenty-three balls when Larry draws?

Continue the table I explained above. You'll be able to "see" the answer directly.

For part d, I say the answer is 7/24. This is my answer after spotting the words "before Jack drew" as you stated above. Am I right now?
 
c) I agree with your solution.

d) Unless they're all putting their balls back into the bag (and the exercise does not state this), I'm not sure how you're getting that there are more balls now than when Jack or Peter drew...?

You put "Peter" in the sixth-row, "glow" column space. What do you have as the entries in the last (seventh) line of the table?

Eliz.
 
Okay...Is this right?

Denis stated:

"Yes, there are still 7 glowers left: we know Jack didn't pick one; he got a striped;
But there are now 21 balls left: 3 have been picked by Janet, Jack and Peter.
OK?"

After reading this statement, I came up with the answer 7/21 = 1/3 for part d of this question. Is this correct?
 
Re: Stapel...My Reply

GWS said:
For part d, I say the answer is 7/24. This is my answer after spotting the words "before Jack drew" as you stated above. Am I right now?
Click to expand...

all stapel was telling you is that there were 23 balls before Jack drew;
so there are 22 left after he drew...don't complicate things 8-)
 
Re: Okay...Is this right?

GWS said:
Denis stated:
"Yes, there are still 7 glowers left: we know Jack didn't pick one; he got a striped;
But there are now 21 balls left: 3 have been picked by Janet, Jack and Peter.
OK?"
After reading this statement, I came up with the answer 7/21 = 1/3 for part d of this question. Is this correct?
Click to expand...
YES!!! Amen :evil:
 
Got it...I think

Okay...there are 22 balls remaining. So, my answer is 7/22 for part d. What about now?
 
Re: Got it...I think

GWS said:
Okay...there are 22 balls remaining. So, my answer is 7/22 for part d. What about now?
Click to expand...
Geezzz GWS, make up your mind: since when is 24 - 3 = 22?
 
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