UNR, MATH/STAT 352, Spring 2007
UNR, MATH/STAT 352, Spring 2007
Radar target detection
How reliable is the signal
on the screen?
(Is it a target of a false alarm?)
UNR, MATH/STAT 352, Spring 2007
Medical screening
How reliable is the positive test?
(Is it a disease or a false alarm?)
UNR, MATH/STAT 352, Spring 2007
How does probability help
to answer such questions?
UNR, MATH/STAT 352, Spring 2007
Deck of playing cards (52 cards)
Four suits
hearts
spades
Thirteen cards in each suit
2,3,4,5,6,7,8,9,10,J,Q,K,A
Faces:
clubs
Jack, Queen, King
diamonds
UNR, MATH/STAT 352, Spring 2007
Deck of playing cards
Sample space for “taking one card at random from a deck”
UNR, MATH/STAT 352, Spring 2007
Is a randomly chosen card
the Queen of Spades?
P(Q♠) = 1/52 ≈ 0.02
UNR, MATH/STAT 352, Spring 2007
Is a randomly chosen card
a Queen?
P(Q) = 4/52 =1/13 ≈ 0.08
UNR, MATH/STAT 352, Spring 2007
Is a randomly chosen RED card
a Queen?
P(Q|red) = 2/26 =1/13 ≈ 0.08
UNR, MATH/STAT 352, Spring 2007
Is a randomly chosen FACE card
a Queen?
P(Q|face) = 4/12 =1/3 = 0.33
UNR, MATH/STAT 352, Spring 2007
Is a randomly chosen SPADES card
a Queen?
P(Q|♠) = 1/13 = 0.08
UNR, MATH/STAT 352, Spring 2007
Event of interest: random card is a Queen
P(Q) = 4/52 =1/13 ≈ 0.08
Some information does not change the chances for the event:
P(Q|red) = 2/26 =1/13 ≈ 0.08
P(Q|♠) = 1/13 = 0.08
… while some does:
P(Q|face) = 4/12 =1/3 = 0.33
UNR, MATH/STAT 352, Spring 2007