are you expert in probability then help me 10 points?

Question

b)A bag contains 10 balls numbered from 1 to 10 without duplicates. Two balls are picked one after another. What is the probability that the first ball’s number is smaller than the second ball?

Answer 1

Since there are no duplicate balls, your chance of picking a smaller ball on the first ball vs. the second ball is 50%.

The reason is because any ball you can pick 1st then 2nd, you can also pick in reverse order. So half of the time it'll be higher and half the time it'll be lower! :-)

Answer 2

i am sorry, 0.5 IS the RIGHT answer but the reasoning provided be some people is incorrect. Suraj read the question incorrectly - he assumed the second ball's number is smaller than the first when the questions states the exact opposite.

wysley used permutations and mentioned 9! = 45, which is incorrect. The correct answer to 9! = 9x8x7x6x5x4x3x2x1 (use your calculator)

as for this question now let's analyse it in detail if you want the FIRST ball's number to be less than the SECOND ball

let's say you pick "1" as the first ball -probability is 1/10. Now if you pick ANY ball afterwards, it will be greater than "1". SInce there are 9 balls left, there is a 100% chance that the next ball will chosen will be GREATER than "1" or a 10% chance for this scenerio. i.e. 9/90

What if you pick "2" on the first draw. Well then you still have only 9 balls left but only 8/9 will be greater than "2". The probability for this scenerio is 1/10 x 8/9 = 8/90. So the answer is 9+8+7+6+5+4+3+2+1+0/90 = 45/90 = 0.5

Answer 3

Two balss are picked one after another. Then the following cases arise.

If the first ball picked up is 1 then the second ball can never be smaller than 1.

First ball picked is 2, probability = 1/10
second ball picked is less than 2 i.e. 1, probability = 1/9
overall probability = 1/10*1/9 = 1/90

first ball picked is 3, probability = 1/10
second ball picked is less than 3 i.e. 1 or 2, probability = 2/9
overall probability = 1/10 * 2/9 = 2/90

If we go on like this till 10 we will get probabilities like 3/90, 4/90, 5/90, 6/90, 7/90, 8/90, 9/90

If we add them up = (1+2+3+4+5+6+7+8+9)/90
= 45/90
= 1/2

Hence the probability that the first ball’s number is smaller than the second ball = 1/2

Answer 4

The answer 0.5 or 50% as given by earlier 'answerers' is correct. Though I would like to share how I figured out the answer.

Firstly, we are given 10 numbered balls, of which we drawn two without replacement. Therefore, how many ways can this be done?

Imagine the first ball we draw is '1', then there are 9 ways we can draw the next ball i.e. '2' to '10'. Similarly, if the first ball is '2', there are also 9 ways we can draw the next ball i.e. '1' and '3' to '10'.

Conclusion, there are 10 times 9 = 90 possible ways to drawn two balls without replacement. (Note: 100 ways With Replacement)

Next, consider the following:

Imagine the first ball we draw is '1', then there are 9 ways in which the next ball is numbered greater than 1 i.e. '2' to '10'. Subsequently, if the first ball is '2', there are 8 ways in which the next ball is numbered greater than 1 i.e. '3' to '10'.

This carries on until we imagine the first ball we draw is '10'. There is No possibility that the next ball will be greater than '10'.

Conclusion, there are (1+2+3+4+5+6+7+8+9) or 45 ways in which the number on the 2nd ball can be greater than the 1st.


Therefore, the probability is computed by 45/90 = 0.5

Answer 5

1 in 10

Answer 6

An easier way to figure this out.
if you pick out a 1 you cannot pick lower - if you pick out a 10 you cannot pick higher - this cancels each other out.
if you pick a 2 then there is only one lower; if you pick out a nine there is only one higher - again one cancels the other out;
in this way you can offset one probablity with another:-
3-7
4-6 which leave you with 5 ball
If you pick the five ball you have 4 above and four below - so the answer is 50-50 or 50% chance.

Answer 7

There is a 50% probability that the first ball is smaller than the second.

Answer 8

Hellow friend, If balls are drawn with out replacement the above answers are correct but with replacement the above said answers are wrong.
If the balls are replaced after drawn. Then total number of possible choices = 45 (not 90).

Hai friend just Know the differece between the probability with replacement and without replacement.

For better understanding more detailes:

http://www.futureaccountant.com/probability/

http://www.schoolingkids.com/probability/

Answer 9

lets start by numberin ur balls 1,2,3,4,5,6,7,8,9,10. out of 10, nine of ur balls av a smaller number than at least one ball ie ball no 9 is smaller than ball no 10, no 8 is larger than 9 and 10.ball no 7 is smaller than 8,9,10 etc. so th probability shld b 9/10

Answer 10

2 to 1 against.