Answer:
P ( P U T ) = 0.6481
Dependent events
P ( P / T ) = (359/756) = 0.4749
Step-by-step explanation:
Given:
- Pink : P
- Teenagers: T
Find:
- P( T u P )
- Are the events T and R dependent, independent, mutually exclusive, or complementary
- If the events are independent, then we can compare P ( P / T ).
Solution:
a)
For first part we will determine the total outcome for T and P:
Total outcomes P or T = 359 + 252 - 121 = 490
(P U T) = (P) + (T) - (P n T)
The total number of possible outcomes are = 756
Hence, P ( P U T ) = 490 / 756 = 0.6481
b)
We are to investigate how the two events are related to one another:
- Check for dependent events:
P ( T n P ) = P( T ) * P ( P / T )
(121 / 756 ) = (252/756) * ( 121 / 252 )
(121 / 756) = (121/756) ....... Hence, events are dependent
- Check for independent events:
P ( T n P ) = P( T ) * P ( P )
(121 / 756 ) = (252/756) * ( 359 / 756 )
(121 / 756) =/ (359/756) ....... Hence, events are not independent
- Check for mutually exclusive events:
P ( T U P ) = P( T ) + P ( P )
(490 / 756 ) = (252/756) + ( 359 / 756 )
(121 / 756) =/ (611/756) ... Hence, events are not mutually exclusive
Hence, the two events are dependent on each other.
c)
If the events are said to be independent then the event:
P ( P / T ) = P (P)
P ( P / T ) = (359/756) = 0.4749
