If A and B are events that have outcomes in common, then P(AorB) = P(A)+P(B)-P(AandB).
11/25 or 44 %
Practice makes perfect
Events are mutually exclusive when they cannot occur at the same time. Or, they are considered overlapping when they have outcomes in common. The following rules apply for the probability of these types of compound events.
Mutually Exclusive Events
Overlapping Events
P(AorB)= P(A)+P(B)
P(AorB)= P(A)+P(B)-P(AandB)
Let A be student is a junior and B be student is on the debate team. Since some students are both a junior and on the debate team, these events are not mutually exclusive. Now, we can find the number of students on the debate team and the number of juniors on the debate team in the given table.
Club
Soph.
Junior
Senior
Totals
Key
12
14
8
12+14+8=34
Debate
2
6
3
2+ 6+3= 11
Math
7
4
5
7+4+5=16
French
11
15
13
11+15+13=39
There are 11 students on the debate team. Out of these, 6 students are juniors. Next, we can calculate the number of juniors and the number of all students in the table.
Club
Soph.
Junior
Senior
Totals
Key
12
14
8
34
Debate
2
6
3
11
Math
7
4
5
16
French
11
15
13
39
Totals
12+2+7+11=32
14+ 6+4+15= 39
8+3+5+13=29
34+ 11+16+39= 100
Now, we know that there are 39 junior students, 11 students on the debate team, 6 junior students on the debate team, and 100 students in total. Finally, we can calculate P(A), P(B), and P(AandB).
P(A)&=39/100 l← ← lJunior students Total students
P(B)&=11/100 l← ← lDebate team Total students
P(AandB)&=6/100 l← ← lJuniors and debate team Total students
With this information we want to find the value of P(AorB).
