Exercise 14 Page 929

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).

P(AorB)=P(A)+ P(B)-P(AandB)

SubstituteValues

Substitute values

P(Aor)= 106/300+ 104/300- 42/300

▼

Simplify right-hand side

AddSubFrac

Add and subtract fractions

P(AorB)=168/300

ReduceFrac

a/b=.a /12./.b /12.

P(AorB)=14/25

▼

Convert to percent

CalcQuot

Calculate quotient

P(AorB)=0.56

WritePercent

Convert to percent

P(AorB)=56 %

The probability that a player is 14 or plays basketball is equal to 1425, which can be also written as 56 %.