who can help me with these questions??
Choices of foods
Quality of buffet
Limited Variety Totals
Good 240 100 340
Bad 175 35 210
Totals 415 135 550
Q1. Given that you know the quality of buffet is bad, compute the probability that it offers limited choices of foods.
P(Bad quality) = 210/550. Conditional probability states that P(A|B) = P(A N B )/P(B).. IN this case let's assume P(A) = Probability of limited choices of food. That makes P(A N B) = 175/550. Applying the formula now, you should get 175/210.
but then again, since you're given a nice table like this one. Another way to do this is to let Total number of outcomes be 210 (Bad quality). Then whats the probabilitty of having limited choices? Probability = No. of success/No. of Outcomes = 175/210
hihi, thanks for explaining to me, i can understand much better already.. : D
I also need help in another question..
1. In a lucky draw, 3 prizes are selected at random from a container that comprises gifts wrapped in 3 colours mainly 2 yellow, 4 red and 4 green. Calculate the probability that
(a) 3 gifts drawn are different colours,
(b) 3 gifts drawn are of same colours.
(c) Suppose you draw one gift at random and discover that it is red, you replace the gift to the container and record your observation. Do you think it will affect your chance of choosing a red gift on your second draw? Explain your reason
2. Workers are paid an average salary of $3.50 per hour with a standard deviation of 50 cents. Suppose the salary is normally distributed. (a) Calculate the probability that the workers are paid between $2.50 and $3.85 per hour. (b) Calculate the minimum salary of highest 4%
(c) State the central limit theorem in your own words. Give example used in such theorem.
i having a hard time understanding the questions.. : D
1a) Is this saying that all are of different colours or just some?
If all different colours, so choose 1st of 1 color, then 2nd and 3rd each of new colours. 3 ways to choose.
3 x 2/10 x 4/9 x 4/8 = 2/15
Otherwise, do same colours first.
b) Only 2 ways where all 3 are of same colours, so...
2 x 4/10 x 3/9 x 2/8 = 1/15
Then chances where 3 gifts are of different combinations (with some same colours) is 14/15.
c) I think this one shouldn't affect at all, since you do replace the gift.
: D thanks so much.. but the 1a) the answer is 4/15 but i cant derive with the answer after drawing the tree diagram.. : D 3 picks are of different colours..
For part (a)
There are 2 ways of looking at it.
The first is to use permutation and combination.
There are a total of 2C1 x 4C1 x 4C1 ways to pick 1 red, 1 green and 1 yellow.
There are a total of 10C3 ways to pick 3 gifts from 10.
so probability = Number of sucess/ Number of ways = (2C1 x 4C1 x 4C1)/10C3
The second way is to consider 1 possible way, that is to pick for instance, Red first, den YEllow, den green.
The probability is (4/10) x (4/9) x (2/8) *number at the denominator gets smaller since its not not replaceable in this question
There are 3! possible ways to pick Red, Yellow, Green in different orders, each of them has a probability of (4/10) x (4/9) x (2/8)
So probability is (4/10) x (4/9) x (2/8) x 3!
You should get the same answer
For part (b)
If they are the same colour, they are either 3red or 3green
lets consider 3 Red, the probability is (4 x 3 x 2)/(10x 9 x 8), Again, its not replaceable
The probability of picking 3 Green is the same.. (4 x 3 x 2)/(10x 9 x 8)
Now you either Pick 3 red OR 3 green to satisfy the requirement of this question
Since its either or (They are mutually Exclusive), You add up the probability. That gives you [(4 x 3 x 2)/(10x 9 x 8)] x 2
For part (c)
I'll leave this part for you to think about =P Think along the lines of what is an independent event?
For question 2,
Let X be the worker's pay,
so X ~ N(3.50, 0.50²)
From here, you can either use your GC, or the traditional method,
P( 2.50 < X < 3.85 ) = P ( X < 3.85 ) - P( X < 2.50 ) *Try to sketch the normal curve here if you can't visualise, I can't show it to you with plain text.
From there, if you want to use the traditional method, you have to normalise it
Meaning, P ( X < 3.85 ) = P ( Z < (3.85 - mean )/ 0.50 )
do the same for P ( X < 2.50 ), Take the difference. =P
For 2 (b) , You can also either use the InvNORM function in your GC, or use the table *not sure what you've been taught.
If you want to use the GC, just use the INV norm function, The input should be ( 0.96, mean, standard deviation ) ====> The first input is the probabilty of X lesser than a critical value.
Your GC can only compute the critical value for X such that P(X< Xc) = 0.96 .. if you know what I mean, It helps you find Xc
That value is 4.32. Which means to say there is a 96% chance that a randomly chosen person has income below that amont.
That value is also the minimum value of the top 4% income earners.
Write back if you don't understand
Originally posted by ThunderFbolt:1a) Is this saying that all are of different colours or just some?
If all different colours, so choose 1st of 1 color, then 2nd and 3rd each of new colours. 3 ways to choose.
3 x 2/10 x 4/9 x 4/8 = 2/15
Otherwise, do same colours first.
b) Only 2 ways where all 3 are of same colours, so...
2 x 4/10 x 3/9 x 2/8 = 1/15
Then chances where 3 gifts are of different combinations (with some same colours) is 14/15.
c) I think this one shouldn't affect at all, since you do replace the gift.
There is 3! ways to pick, which means 6 ways. Not 3.
hihi, hmm.. for question 2 i dont really understand the solution given. what does a GC means? X~N(3.50, 0.50) is what kind of concept? : D
Normal Distribution, have you not been taught?
Wait a minute.. what level are you studying?
basics of business statistics.. i have only learnt until Binomial distribution and poisson distribution haven learn until normal distributions.. : D i studying diploma level.. : D
That is clearly a question that test you on normal distribution. Your lecturer probably haven't gone through it with you yet, I believe he/she will. There's no other way to do this without any prior knowledge.
hmm.. that is bad.. he haven teach than give a assigment that want us to pass up today... : D no wonder i dont really understand the solutions.. : D
He's totally messed up on his part then... lol. goes to show he didn't look through the work he's given out