probability help (1 Viewer)

[Mr Chi]

i need help with this question...

A manufacturer of X brand soft drink surveyed a city and found 31 people like X drinks best, 19 liked another brand better and 5 did not drink soft drink. If any two people are selected at random from that city, find the probability that

a) one person would like the X brand of soft drink
b) both people would not drink soft drink

Also, can anyone tell me all the basic rules in the probability chapter, that would be much appreciated thanks.

 

[SoulSearcher]

I hate probability but I'll do it anyway.

(a) P(1 person like brand X) = (31/55 * 24/54) + (24/55 * 31/54)
= 124 / 495 + 124 / 495
= 248 / 495

(b) P(no one drinks soft drink) = 5 / 55 * 4 /54
= 2 / 297

General rules when dealing with probability trees:
- add going down a branch
- multiply across branches
Not sure about other rules though, I'll let other people give you those ones.

 

[SoulSearcher]

Yes true, and so let us assume that the city only contains 55 people. But if the question happens to be different, I shall alter my answer to fit the new conditions.

 

[Riviet]

If any two people are selected at random from that city

In my opinion, the wording in that phrase would suggest that you are selecting without replacement. Usually in questions, they will specify if there is replacement involved [to avoid any ambiguities or confusion]. If there is no mention of the word "replacement" in the question, I would assume that there is no replacement.

 

[Nerd Queen]

I agree ... I think this is a replacement question ... in any case here is what i got ... but i always sucked at probability

a) P(x<u><b>x</u></b>) = 31/55 * [(19+5)/55]*2
= [744/3025]*2
= 0.492 or 49.2%

b) P(NN) = 5/55 *5/55
= 25/3025
= 0.00826 or 0.8%

well thats what i gathered anyways might be wrong ... but heres what i did

a) you times the probability of liking x with the probability of not. Assume that other softdrink is Y and people who dont drink softdrink are n. Then the probability of people not likikg x will be P(Y) + P(N) ... which is as it turns out (19+5)/55. so u multiple this by P(x) ... PS- here the underlined x meant NOT X (And you gotta multiply it by two because u can either have P(x<b><u>x</b></u>) or P(<b><u>x</b></u>x) - thanx soulsearcher)

b) simply the probability of N times the probability of N ... in other words P(N)*P(N)

Well, hope i was right n hope that helped.

 

[SoulSearcher]

One little problem with (a). Remember that the first person might not like brand X and the second person does, so you would have to multiply your final answer by 2 to get it correct. Otherwise your working out is fine if this is a replacement question.

 

[Nerd Queen]

o yea ... thanx ... well at least i told u i suck at probability ... totally forgot about that ... fixed up now