Mutually Exclusive Events
OBJ: • Find the probability that
mutually exclusive and
inclusive events occur
Addition Rule
P (A or B)
P (A and B)
P (A U B) =
P (A ∩ B)
P(A) + P(B)–P(A∩B)
DEF: Mutually Exclusive Events
2 events that
cannot both occur
at the same time;
P (A and B) = 0
P (A ∩ B) = 0
Impossible event
P (A or B)
P(A U B)=P(A)+P(B)
EX:  In a throw of 2 dice, what
is the probability of obtaining a
sum of 7 or 11
6
(sums of 7)
36
(sums)
2
3
4
5
6
7
3
4
5
6
7
8
2
36
4
5
6
7
8
9
5
6
7
8
9
10
6
7
8
9
10 11
7
8
9
10 11 12
(sums of 11)
(sums)
6 + 2
36
36
8
36 =
2
9
EX:  In a throw of a red die, r,
and a white die, w, find:
P (sum of 6 or sum of 10)
5
(sums of 6)
36
(sums)
3
36
(sums of 10)
(sums)
5 + 3
36
36
8
36 =
2
9
2
3
4
5
6
7
3
4
5
6
7
8
4
5
6
7
8
9
5
6
7
8
9
10
6
7
8
9
10 11
7
8
9
10 11 12
DEF:  Inclusive Events
2 events that can
both occur at the
same time
P (A or B)
P (A U B) =
P(A) + P(B)–P(A∩B)
EX:  In a throw of a red die, r,
and a white die, w, find:
P (r ≤ 3 or w = 2)
18
36
6
36
P (r ≤ 3)
(r  3)
(die pairs)
P (w = 2)
(w = 2)
(die pairs)
P (r ≤ 3 and w = 2)
P (r  3 ∩ w = 2)
3
36
P (r ≤ 3 or w = 2)
P (r ≤ 3) + P (w = 2)–P (r ≤ 3 ∩ w = 2)
18 + 6 – 3
36 36 36
21
36
7
12
(1, 1)
(1,2)
(1, 3)
(1, 4)
(1, 5)
(1, 6)
(2, 1)
(2, 2)
(2, 3)
(2, 4)
(2, 5)
(2, 6)
(3, 1)
(3, 2)
(3, 3)
(3, 4)
(3, 5)
(3, 6)
(4, 1)
(4, 2)
(4, 3)
(4, 4)
(4, 5)
(4, 6)
(5, 1)
(5, 2)
(5, 3)
(5, 4)
(5, 5)
(5, 6)
(6, 1)
(6, 2)
(6, 3)
(6, 4)
(6, 5)
(6, 6)
EX:  In a throw of a red die, r,
and a white die, w, find:
P (r ≥ 3 or w ≥ 5)
24
36
12
36
P (r ≥ 3)
(r  3)
(die pairs)
P (w ≥ 5)
(w  5)
(die pairs)
P (r ≥ 3 and w ≥ 5)
P (r  3 ∩ w  5)
8
36
P (r ≥ 3 or w ≥ 5)
P (r ≥ 3) + P (w ≥ 5)–P (r ≥ 3 ∩ w ≥ 5)
24 + 12 – 8
36 36 36
28
36
7
9
(1, 1)
(1,2)
(1, 3)
(1, 4)
(1, 5)
(1, 6)
(2, 1)
(2, 2)
(2, 3)
(2, 4)
(2, 5)
(2, 6)
(3, 1)
(3, 2)
(3, 3)
(3, 4)
(3, 5)
(3, 6)
(4, 1)
(4, 2)
(4, 3)
(4, 4)
(4, 5)
(4, 6)
(5, 1)
(5, 2)
(5, 3)
(5, 4)
(5, 5)
(5, 6)
(6, 1)
(6, 2)
(6, 3)
(6, 4)
(6, 5)
(6, 6)
EX:  A card is drawn from an
ordinary deck. Find:
P (red or a queen)
26 + 4 – 2
52
52 52
28
52
7
13
P(black king or a club)
2 + 13 – 1
52 52 52
14
52
7
26
EX:  A card is drawn from an
ordinary deck. Find:
P(an even number or black)
P (red face or a jack)
20 + 26 – 10
52
52
52
36
52
9
13
6 + 4 – 2
52 52 52
8
52
2
13
EX:  In a throw of a red die, r,
and a white die, w, find:
Worksheet
1.
P (sum = 7 or red die = 3)
P (sum = 7)
6
36
P (red die = 3)
6
36
P (sum = 7 and red die = 3
1 • 1
6
6
6 + 6 – 1
36 36 36
11
36
(1, 1)
(1,2)
(1, 3)
(1, 4)
(1, 5)
(1, 6)
(2, 1)
(2, 2)
(2, 3)
(2, 4)
(2, 5)
(2, 6)
(3, 1)
(3, 2)
(3, 3)
(3, 4)
(3, 5)
(3, 6)
(4, 1)
(4, 2)
(4, 3)
(4, 4)
(4, 5)
(4, 6)
(5, 1)
(5, 2)
(5, 3)
(5, 4)
(5, 5)
(5, 6)
(6, 1)
(6, 2)
(6, 3)
(6, 4)
(6, 5)
(6, 6)
2
3
4
5
6
7
3
4
5
6
7
8
4
5
6
7
8
9
5 6 7
6 7 8
7 8 9
8 9 10
9 10 11
10 11 12
EX:  In a throw of a red die, r,
and a white die, w, find:
Worksheet
2.
P (sum = 10 and red die = 4)
P (sum = 10)
3= 1
(reduce since multi.)
36 12
P (red die = 4)
6= 1
36 6
1 • 1
12 6
2(1/72)
1
36
(and →multiply)
(1, 1)
(1,2)
(1, 3)
(1, 4)
(1, 5)
(1, 6)
(2, 1)
(2, 2)
(2, 3)
(2, 4)
(2, 5)
(2, 6)
(3, 1)
(3, 2)
(3, 3)
(3, 4)
(3, 5)
(3, 6)
(4, 1)
(4, 2)
(4, 3)
(4, 4)
(4, 5)
(4, 6)
(5, 1)
(5, 2)
(5, 3)
(5, 4)
(5, 5)
(5, 6)
(6, 1)
(6, 2)
(6, 3)
(6, 4)
(6, 5)
(6, 6)
2
3
4
5
6
3
4
5
6
7
4
5
6
7
8
5
6
7
8
9
6 7
7 8
8 9
9 10
10 11
EX:  In a throw of a red die, r,
and a green die, g, find:
Worksheet
4.
P (r > 5 or g < 2)
P (r > 5)
6
36
P (g < 2)
6
36
3.
1 •
6
6 +
36
11
36
P (r > 5 and g < 2)
(and →multiply)
1
6
6 – 1
36 36
(1, 1)
(1,2)
(1, 3)
(1, 4)
(1, 5)
(1, 6)
(2, 1)
(2, 2)
(2, 3)
(2, 4)
(2, 5)
(2, 6)
(3, 1)
(3, 2)
(3, 3)
(3, 4)
(3, 5)
(3, 6)
(4, 1)
(4, 2)
(4, 3)
(4, 4)
(4, 5)
(4, 6)
(5, 1)
(5, 2)
(5, 3)
(5, 4)
(5, 5)
(5, 6)
(6, 1)
(6, 2)
(6, 3)
(6, 4)
(6, 5)
(6, 6)
EX:  In a throw of a red die, r,
and a green die, g, find:
8. P (sum is prime or sum <6)
P (sum is prime)
15
(prime sums)
36
(sums)
P (sum <6)
10
(sums < 6)
36
(sums)
P (sum is prime & sum < 6)
7
36
15 + 10 – 7
36 36 36
18/36 = ½
2
3
4
5
6
7
3
4
5
6
7
8
4
5
6
7
8
9
5
6
7
8
9
10
6
7
8
9
10 11
7
8
9
10 11 12
EX:  A card is drawn from an
ordinary deck. Find:
Worksheet
(9) P (king or club)
4 + 13 – 1
(10)
52 52 52
16
52
4
13
Worksheet
(11) P (king or queen)
4 + 4
(12) 0
52 52
8
52
2
13
Worksheet: Select a number
between 1 and 100 (inclusive)
(18) P (prime)
25
100
1
4
(19) P (less than 50)
49
100
(20) P (prime and < 50)
15
100
3
20
(21) P (prime or < 50)
25 + 49 – 15
100 100 100
59
100