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



Radar target detection

How reliable is the signalon the screen?

(Is it a target of a false alarm?)


How reliable is the positive test?(Is it a disease or a false alarm?)

Medical screening


How does probability help to answer such questions?


Deck of playing cards (52 cards)

Four suits

Thirteen cards in each suit

2,3,4,5,6,7,8,9,10,J,Q,K,A

Faces:

Jack, Queen, King

hearts

spades

diamonds

clubs


Deck of playing cards

Sample space for “taking one card at random from a deck”


Is a randomly chosen cardthe Queen of Spades?

P(Q♠) = 1/52 ≈ 0.02


Is a randomly chosen carda Queen?

P(Q) = 4/52 =1/13 ≈ 0.08


Is a randomly chosen RED carda Queen?

P(Q|red) = 2/26 =1/13 ≈ 0.08


Is a randomly chosen FACE carda Queen?

P(Q|face) = 4/12 =1/3 = 0.33


Is a randomly chosen SPADES carda Queen?

P(Q|♠) = 1/13 = 0.08


P(Q|face) = 4/12 =1/3 = 0.33

P(Q) = 4/52 =1/13 ≈ 0.08

P(Q|red) = 2/26 =1/13 ≈ 0.08

P(Q|♠) = 1/13 = 0.08

Some information does not change the chances for the event:

… while some does:

Event of interest: random card is a Queen

Documents

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?)