Download Finite Math section 7.5 Independent Events Def P(E F) Def Events E

Finite Math
section 7.5
Def
Def
Independent Events
P(EF) ´
P(E∩F)
P(F)
Events E and F are independent if P(EF) = P(E) or P(FE) = P(F)
Thm: Events E and F are independent if and only if P(E ∩ F) = P(F) † P(E)
Summary: 3 ways to check if events E and F are independent.
(1) P(EF) = P(E) OR (2) P(FE) = P(F) OR (3) P(E ∩ F) = P(F) † P(E)
Note: (1)
(2)
(3)
(4)
Ex1,
P(E ∩ F) = P(F) † P(EF)
P(E ∩ F) = P(F) † P(E)
P(E ∩ F) = P(E) † P(FE)
P(E ∩ F) = P(E) † P(F)
This is always true.
This is true only when E and F are independent.
This is always true.
This is true only when E and F are independent.
There are 60 students in a class room. 40 students commute by car. 20 students do NOT commute by car.
22 students wear glasses and commute by car. 11 students wear glasses and do not commute by car.
1 student is randomly selected.
(a) Construct the frequency chart. (or probablity chart = relative frequency chart.)
(b) Is commuting by car and wearing glasses independent?
(Is the event that the 1 randomly selected student commutes by car and
the event that the 1 randomly selected student wears glasses independent?)
Ex2,
There are 200 students. 80 students are taking English and 70 students taking math. 30 students taking
both math and English. One student is selected randomly.
(a) Construct the frequency chart and relative frequency chart (= probability chart when 1 person is selected)
(b) Is taking math and taking English independent events?
Ex3,
Game 1:
Game 2:
Roll a die once. If the die is 4 or higher, then you win a candy.
Roll a die until the die is even. If the die is 4 or higher, then you win a candy.
(a) Find the probability that you win a candy from Game 1.
(b) Find the probability that you win a candy from Game 2.
Ex3,
1 die is rolled.
(a) Is the event where the die is 5 or 6 and the event where the die is even independent?
(b) Is the event where the die is 4 or higher and the event where the die is even independent?
(c) Is the event where the die is 4 or higher and the event where the die is 1 or 2 independent?
(d) Is the event where the die is 4 or higher and the event where the die is 1 or 2 mutually exclusive?
( Events E and F are mutually exclusive if E ∩ F = 
(same as n(E ∩ F) = 0, same as P(E ∩ F) = 0) )