A game show involves three doors. One door conceals a brand new car, and the other two doors conceal rubber chickens. To start the game, the contestant picks one of the doors. The host then opens one of the other doors, revealing a rubber chicken. Finally, the contestant is given the option to either open the door they have chosen, or switch and open the other door. Using the Law of Total Probability, explain why the contestant will double their chances of winning the car if they switch doors.
A game show involves three doors. One door conceals a brand new car, and the other two doors conceal rubber chickens. To start the game, the contestant picks one of the doors. The host then opens one of the other doors, revealing a rubber chicken. Finally, the contestant is given the option to either open the door they have chosen, or switch and open the other door. Using the Law of Total Probability, explain why the contestant will double their chances of winning the car if they switch doors.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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Question
Using law of total probability on second pic. Cannot use any idea of conditional probability. Thanks
Transcribed Image Text:3. A game show involves three doors. One door conceals a brand new car, and
the other two doors conceal rubber chickens. To start the game, the contestant
picks one of the doors. The host then opens one of the other doors, revealing
a rubber chicken. Finally, the contestant is given the option to either open
the door they have chosen, or switch and open the other door. Using the Law
of Total Probability, explain why the contestant will double their chances of
winning the car if they switch doors.
Transcribed Image Text:Mope genekally by induetion do
Theskems If i An are patreise dirjdattAr Alj=p
then
Pt
na
☺ Ad = Ž PLA)
taw of totat Probublits( LoTP)
i Let EClbe an event Let A, An be a purtia of R Lthat is ,
a pairmise disjadat collecton bf sets that laver i the Sample spuca ☺ Ą=N)
Then: PLE): E OP LENA).
Phof: E= LEOAJ V LENA)U
U LEnAn)
apply.
0,00 ate stilt paimise disjotnt ,
Hence PLEL
choase A wis wil make ploblens casar
PLEAA
important spodat case?
P LAL= PLADB) + PLANB)
stare BB is a pattùn of qud ak paikalse dsbit
The em: PCAUB J = PLAD t PLB) - PLANB)
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