Probability with pairs of things

[mutzy188]

Homework Statement

The five numbers 1, 2, 3, 4, and 5 are written respectively on five disks of the same size and placed in a hat. Two disks are drawn without replacement from the hat, and the numbers written on them is observed.

(a) List the 10 possible outcomes for this experiment as unordered pairs of numbers.


(b) If each of the 10 outcomes has probability 1/10, assign a value to the probability that the sum of the two numbers drawn is (i) 3, (ii) between 6 and 8 inclusive

The Attempt at a Solution

(a)
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5

(b)

(i)

That would be the pair: 1 2

The probability of drawing a 1 and a 2 is: 1/10


(ii)

That would be the pairs:

1 5
2 4
2 5
3 4
3 5
4 5

This probability would be: (1/10)^6

Thanks

 

[neutrino]

Check the your second answer in b.

(ii)

That would be the pairs:

1 5
2 4
2 5
3 4
3 5
4 5

This probability would be: (1/10)^6

 

[mutzy188]

Check the your second answer in b.

How would I go about finding the probability for that one

 

[wbclark]

It is only to correct to multiply probabilities if you're trying to find the probability of ALL of these things happen. In other words, if you needed to draw first the pair 1 5, then 2 4, then 2 5, etc.

However, the condition is that ONE of these combinations is drawn in ONE trial, so you add the probabilities.

 

[HallsofIvy]

(1/10)⁶ is the probability that you drew those specific pairs in 6 consectutive drawings (with replacement).

The probability of drawing one of those is the number of such outcomes, 5, divided by the total number of outcomes, 10. Of course, that is exactly the same as adding the probability of each, as wbclark said.

 

[neutrino]

How would I go about finding the probability for that one

It is only to correct to multiply probabilities if you're trying to find the probability of ALL of these things happen. In other words, if you needed to draw first the pair 1 5, then 2 4, then 2 5, etc.

However, the condition is that ONE of these combinations is drawn in ONE trial, so you add the probabilities.

To add to that, 4 and 5 make 9.

 

[HallsofIvy]

Picky, picky!