Consider the experiment of placing three distinguishable particles (which we den
ID: 3354617 • Letter: C
Question
Consider the experiment of placing three distinguishable particles (which we denote by a, b, and c) into W2 = (a cl b |-), etc. a) Write down the sample space . How many sample points are there in Q2 b) Let events A, B, C be defined as three cells. Examples of sample points are on = (a b c1-1-), A- multiple particles occupy a cell; B- the first cell is not empty; C = both A and B occur. How many sample points are there events A, B, and C respectively? Repeat a) and b) if the three particles are indistinguishable. Examples of sample pointsExplanation / Answer
Part (a)
Sample Space
Sample Point #
Particles in cell
1
2
3
1
abc
2
abc
3
abc
4
ab
c
5
ab
c
6
c
ab
7
ab
c
8
c
ab
9
c
ab
10
ac
b
11
ac
b
12
b
ac
13
ac
b
14
b
ac
15
b
ac
16
bc
a
17
bc
a
18
a
bc
19
bc
a
20
a
bc
21
a
bc
22
a
b
c
23
a
c
b
24
b
c
a
25
c
b
a
26
b
a
c
27
c
a
b
Part (b)
Number of sample points in A (multiple particles occupy a cell) 21 ANSWER 1
Details of sample points
Sample Point #
Particles in cell
1
2
3
1
abc
2
abc
3
abc
4
ab
c
5
ab
c
6
c
ab
7
ab
c
8
c
ab
9
c
ab
10
ac
b
11
ac
b
12
b
ac
13
ac
b
14
b
ac
15
b
ac
16
bc
a
17
bc
a
18
a
bc
19
bc
a
20
a
bc
21
a
bc
Number of sample points in B (first cell is not empty) 19 ANSWER 2
Details of sample points
Sample Point #
Particles in cell
1
2
3
1
abc
2
ab
c
3
ab
c
4
c
ab
5
c
ab
6
ac
b
7
ac
b
8
b
ac
9
b
ac
10
bc
a
11
bc
a
12
a
bc
13
a
bc
14
a
b
c
15
a
c
b
16
b
c
a
17
c
b
a
18
b
a
c
19
c
a
b
Number of sample points in C (both A and B occur) 13 ANSWER 3
Details of sample points
Sample Point #
Particles in cell
1
2
3
1
abc
2
ab
c
3
ab
c
4
c
ab
5
c
ab
6
ac
b
7
ac
b
8
b
ac
9
b
ac
10
bc
a
11
bc
a
12
a
bc
13
a
bc
Part (c)
The three particles are in-distinguishable.
Sample Space
Sample Point #
Particles in cell
1
2
3
1
abc
2
abc
3
abc
4
ab
c
5
ab
c
6
c
ab
7
ab
c
8
c
ab
9
c
ab
10
a
b
c
Part (d)
Number of sample points in A (multiple particles occupy a cell) 9 ANSWER 1
Details of sample points
Sample Point #
Particles in cell
1
2
3
1
abc
2
abc
3
abc
4
ab
c
5
ab
c
6
c
ab
7
ab
c
8
c
ab
9
c
ab
Number of sample points in B (first cell is not empty) 6 ANSWER 2
Details of sample points
Sample Point #
Particles in cell
1
2
3
1
abc
2
ab
c
3
ab
c
4
c
ab
5
c
ab
6
a
b
c
Number of sample points in C (both A and B occur) 5 ANSWER 3
Details of sample points
Sample Point #
Particles in cell
1
2
3
1
abc
2
ab
c
3
ab
c
4
c
ab
5
c
ab
Sample Point #
Particles in cell
1
2
3
1
abc
2
abc
3
abc
4
ab
c
5
ab
c
6
c
ab
7
ab
c
8
c
ab
9
c
ab
10
ac
b
11
ac
b
12
b
ac
13
ac
b
14
b
ac
15
b
ac
16
bc
a
17
bc
a
18
a
bc
19
bc
a
20
a
bc
21
a
bc
22
a
b
c
23
a
c
b
24
b
c
a
25
c
b
a
26
b
a
c
27
c
a
b