Respuesta :
Answer:
Event A is having pizza for lunch and B having tacos for lunch. Since [tex]P(A \cap B) = P(A)P(B)[/tex], these two events are independent.
Step-by-step explanation:
Two events, A and B are independent, if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this problem:
Event A: having pizza for lunch.
Event B: having tacos for lunch.
55% chance of kids having pizza for lunch
This means that [tex]P(A) = 0.55[/tex]
20% chance of kids having tacos for lunch
This means that [tex]P(B) = 0.2[/tex]
11% chance of kids having pizza and tacos together for lunch.
This means that [tex]P(A \cap B) = 0.11[/tex]
So
[tex]P(A \cap B) = P(A)P(B)[/tex]
[tex]0.11 = 0.55*0.2[/tex]
[tex]0.11 = 0.11[/tex]
Event A is having pizza for lunch and B having tacos for lunch. Since [tex]P(A \cap B) = P(A)P(B)[/tex], these two events are independent.
Answer:
The two events "kids eating pizza" and "kids eating tacos" are independent.
Step-by-step explanation:
Solution:-
- Denote the following events:
Event ( P ) : kids having pizza for lunch
Event ( T ) : kids having tacos for lunch
- We will interpret each and every statement given in terms of probability of defined events:
- There is a 55% chance of kids having pizza for lunch. Tells us the likely hood of kids having pizza for lunch - Event ( P ) ;
p ( P ) = 0.55
- There is a 20% chance of kids having Tacos for lunch. Tells us the likely hood of kids having Tacos for lunch - Event ( T ) ;
p ( T ) = 0.20
- A 11% chance of kids having pizza and tacos together for lunch. Tells us the likely-hood of two events occurring simultaneously:
p ( T & P ) = 0.11
- We have to investigate whether two defined events ( T ) and ( P ) are independent or not. The condition for independent events is given as:
p ( A & B ) = p ( A ) * p ( B )
- So for the data given to us:
p ( T & P ) = p ( P ) * p ( T )
p ( P ) * p ( T ) = 0.2*0.55 = 0.11
p ( T & P ) = 0.11
Hence,
- The two events Event ( P ) and Event ( T ) are independent events.
