What is the probability?

  • Thread starter gaganpreetsingh
  • Start date
  • Tags
    Probability
The fraction does not change.In summary, the probability that A speaks before B and B speaks before C at the function is 1/6, regardless of the total number of people speaking. This is because there are a total of 3! = 6 possible orders for A, B, C and only one of those orders satisfies the given condition. Therefore, the probability is always 1/6, regardless of the number of other people speaking.
  • #1
gaganpreetsingh
24
0
Three persons A,B,C are to speak at the function along with 5 other persons. If the persons speak in random order, what is the probability that A speaks before B and B speaks before C?

I am unable to begin with calculating the favourable possibilities.
 
Physics news on Phys.org
  • #2
There are 8 persons, call them A, B, C, D, E, F, G, H.

In how many different orderings can you put these 8 people?

How many of these orderings satisfy order(A) < order(B) < order(C)?
 
  • #3
Since all you are concerned with is the position of A, B, C, I don't think you need to worry about the other 5. How many orders for 3 people, A, B, C, are there? How many of those have precisely ABC in that order?
 
  • #4
But, isn't ABDEFGHC a different outcome than ABDEFGCH? By your logic, these two would've counted as one.
 
  • #5
Take the spots that A, B, and C talk in as all the same kind of spot--say X. Then find all the ways to place 3 X's out of 8 spots, and then find how many total ways the other speakers can be arranged once the 3 X's are placed.

Edit: though actually, this will lead to the same answer as what Ivy and Integral said to do.
 
Last edited:
  • #6
EnumaElish said:
But, isn't ABDEFGHC a different outcome than ABDEFGCH? By your logic, these two would've counted as one.

If you consider all 8 people, then, yes, they are different outcomes- and the numerator of the probability fraction will be different than if you only consider A, B, C. But then you would have to consider ACDEFGHB (where they are not in ABC order) as different from ACDEFGBH. The denominator of the fraction is also different- the result is the same.

To take a simple example: suppose there are 4 people, A, B, C, D speaking. What is the probability that A, B, C speak in the order ABC?

There are, of course 4!= 24 different ways to order 4 things:
ABCD ABDC ACBD ACDB ADBC ADCB
BACD BADC BCAD BCDA BDAC BDCA
CBAD CBDA CABD CADB CDBA CDAB
DBCA DBAC DCBA DCAB DABC DACB

Of those, ABCD, ABDA, ADBC, DABC have A, B, C in that order: the probability that A, B, C will speak in that order is 4/24= 1/6.

If instead we count only A, B, C, we find 3!= 6 different orders and only 1 (ABC) has them in that order: Again 1/6.

Given any n people speaking in random order, the probability that a given 3 will speak in a given order is 1!/3!= 1/6. If you use all orders for n people as the denominator and all orders for n people that have the same 3 people in the given order, the numerator and denominator are both multiplied by n!/3!.
 

What is the probability?

The probability is a measure of the likelihood or chance that a particular event will occur. It is usually expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

How is probability calculated?

Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This can be represented as a fraction, decimal, or percentage.

What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes all outcomes are equally likely. Experimental probability is based on actual data and outcomes from an experiment or real-life situation.

How does sample size affect probability?

The larger the sample size, the more accurate the probability calculation will be. This is because a larger sample size provides a more representative sample of the entire population.

What is conditional probability?

Conditional probability is the probability of an event occurring given that another event has already occurred. It is calculated by dividing the probability of the joint event (both events occurring) by the probability of the first event occurring.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
10
Views
1K
  • Precalculus Mathematics Homework Help
Replies
9
Views
1K
  • Precalculus Mathematics Homework Help
Replies
12
Views
941
  • Precalculus Mathematics Homework Help
Replies
2
Views
814
  • Precalculus Mathematics Homework Help
Replies
5
Views
2K
  • Precalculus Mathematics Homework Help
Replies
18
Views
284
  • Precalculus Mathematics Homework Help
Replies
5
Views
830
  • Precalculus Mathematics Homework Help
Replies
2
Views
880
  • Precalculus Mathematics Homework Help
Replies
4
Views
1K
  • Precalculus Mathematics Homework Help
Replies
5
Views
2K
Back
Top