If A and B are events that have outcomes in common, then P(AorB) = P(A)+P(B)-P(AandB).
14/25 or 56 %
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 player is 14 and B be player plays basketball. Since some students are both 14 and play basketball, these events are not mutually exclusive. Now, we can find the number of players aged 14 and the number of basketball players aged 14 in the given table.
Graceland Sports Complex
Age
Soccer
Baseball
Basketball
Total
14
28
36
42
28+36+ 42= 106
15
30
26
33
30+26+33=89
16
35
41
29
35+41+29=105
There are 106 players aged 14. Out of these players, 42 play basketball. Next, we can calculate the number of basketball players and the number of all players in the table.
Graceland Sports Complex
Age
Soccer
Baseball
Basketball
Total
14
28
36
42
106
15
30
26
33
89
16
35
41
29
105
Total
28+30+35=93
36+26+41=103
42+33+29= 104
106+89+105= 300
Now, we know that there are 106 players aged 14, 104 basketball players, 42 basketball players aged 14, and 300 players in total. Finally, we can calculate P(A), P(B), and P(AandB).
P(A)&=106/300 l← ← lAged14 Total players
P(B)&=104/300 l← ← lBasketball Total players
P(AandB)&=42/300 l ← ← lBasketball and aged14 Total players
With this information we want to find the value of P(AorB).
