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?)

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

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 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

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 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