Hmm...... probability again

[wydiwyg]

Probailities

1. What is the probability that 2 people chosen at random were born on the same day of the week.

2. What is the probability that 2 people chosen at random were born on the same month.

3. What is the probability that a number chosen at rando from the primes between 100 and 199 is odd.

4. A jar contains 4 marbles: 2red and 2 white. 2 marbles are chosen at random.
Coln A: The probability that the marbles chosen are the same color.
Coln B: The probability that the marbles chosen are different color.

5. There are 27 studnets on the colege debate team . What is the probability that at least 3 of them have their birthdays in the same month?

A> 0 B> 3/27 C> 3/12 D> 1/2 E> 1


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Combination/Permutation
1.
Coln A: The no of ways to assign a number from 1 to 5 to each of 4 people.
Coln B: The no of ways to assign a number from 1 to 5 to each of 5 people.

2. A jar contains 20 marbles; 4 red . 6 white and 10 blue. If you remove marbles one at a time randomly, what is the number that must be removed to be certain that you have at least 2 marbles of each colour?


Esp,I am expecting elegant and nice explanations from TOP GUN and stickler Nishant.

[Top_Gun]

probability:

1. 1/7

2. 1/12

3. 1

4. B

5. 1

[wydiwyg]

probability:

1. 1/7

2. 1/12

3. 1

4. B

5. 1

That was not what I had expected from you. I want more ludcid explanations dude.

[Top_Gun]

combinations/permutations:

1. B

2. 18.

[Top_Gun]

sorry wydiwyg, I'm facing a lot of problems to get into testmagic. It is taking about 10 mins to open a page( and i'm not even kidding a bit ).

Now, i'll try to give explanations.

1. What is the probability that 2 people chosen at random were born on the same day of the week.

Answer: 1/7.

Just take a random person. The probability that he is born in any day of a week is 1.
Now, take the second person. The probability that he is born exactly the same day that the other person were born is 1/7.

So..the probability that two persons taken in random will be born in the same day of the week = 1 * 1/7
= 1/7.

2. What is the probability that 2 people chosen at random were born on the same month.

Answer: The same way it is: 1/12

3. What is the probability that a number chosen at rando from the primes between 100 and 199 is odd.

Answer: 1.

All the primes between 100 and 199 are certainly odd.
In fact the only even prime is 2( cause otherwise 2 would be a factor of that even number ).

So..the probability must be 1.

4. A jar contains 4 marbles: 2red and 2 white. 2 marbles are chosen at random.
Coln A: The probability that the marbles chosen are the same color.
Coln B: The probability that the marbles chosen are different color.

Answer: B

Just take a ball from the jar either white or red, so the probability is 1.

Then, take the second one.

Now, For column A: the probability is 1/3, cause there r only one ball in the jar that has the same color as the first ball chosen.

For column B: The probability is 2/3 cause there r two balls of the color that is different from the first ball taken out.

So..the answer is B
5. There are 27 studnets on the colege debate team . What is the probability that at least 3 of them have their birthdays in the same month?

A> 0 B> 3/27 C> 3/12 D> 1/2 E> 1

Answer: 1.

In no way u can have 27 persons taken such that no 3 persons were born in the same way. In fact, 27 is redundant here, u can't have even 25 earthlings taken such way.

In the best case, u can take 12 persons of whom each and everyone is born in the same month..Then take another 12 of them. So..at this point, there r 24 earthlings of which every 2 of them were born in the same month. but, when u'll take the 25th person..u've to put him in a month which already has 2 more earthlings. so..this makes it that 3 earthlings were born in that month.

So... the probability is 1.

--------------
Combination/Permutation
1.
Coln A: The no of ways to assign a number from 1 to 5 to each of 4 people.
Coln B: The no of ways to assign a number from 1 to 5 to each of 5 people.

The number of ways u can assign the numbers is:

Col A: 5P4.

COL B: 5!

So... col B is greater.

answer is B.


2. A jar contains 20 marbles; 4 red . 6 white and 10 blue. If you remove marbles one at a time randomly, what is the number that must be removed to be certain that you have at least 2 marbles of each colour?


Answer: 18.

U've to consider the worst case here.

In the worst case, u can respectively remove 10 blue balls...then following with the 6 white balls...and then 2 red balls. Now, u've got 2 marbles of each color. And u've to pull 18 balls.

the key here is to: u've to take all cases into account cause the question says that u've to be absolutely certain that u've at least 2 balls of each color.

Esp,I am expecting elegant and nice explanations from TOP GUN and stickler Nishant.

Answers: Thanks dude for giving me such honor. I hope i'm not mistaken about those answers and i think nishat would not be pretty pleased with it cause u've got his nick wrong( stickler_nishat ).

[rmc]

I agree with Top_Gun on all questions except:
Combination/Permutation
1.
Coln A: The no of ways to assign a number from 1 to 5 to each of 4 people.
Coln B: The no of ways to assign a number from 1 to 5 to each of 5 people.

The number of ways u can assign the numbers is:

Col A: 5!.

COL B: 5!
so that correct answer is C (not B)

[manwiththemission2005]

Coln A: The no of ways to assign a number from 1 to 5 to each of 4 people.
Coln B: The no of ways to assign a number from 1 to 5 to each of 5 people.

The number of ways u can assign the numbers is:

Col A : 5*5*5*5
Col B : 5*5*5*5*5
B is greater.

No condition is mentioned as there shouldn't be repeated numbers..

[Top_Gun]

Oops..

MWM is right. As there was no condition mentioned, we have to consider the cases of repeated numbers. Didn't think of that thing.

[manwiththemission2005]

It doesnt matter.. you got B na?? .. you are right with the wrong method

[seemahesh]

hi all,
what r the right answers????????????


seema