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C = draw a heart
? Are events A & C independent of each other? NUS/FoS/DSAP 9 GEM2900  Understanding Uncertainty & Statistical Thinking Semester 1, 2009/2010 Examples 2
Drawing 5 cards from a deck of 52 cards with replacement
ith
Consider event C = draw a heart
? What is the probability of getting all hearts? ? What is the probability of getting no heart? NUS/FoS/DSAP 10 GEM2900  Understanding Uncertainty & Statistical Thinking Semester 1, 2009/2010 Examples 3
Drawing 5 cards from a deck of 52 cards with replacement
ith
Consider event C = draw a heart ? What is the probability of getting at least one heart? NUS/FoS/DSAP 11 GEM2900  Understanding Uncertainty & Statistical Thinking Semester 1, 2009/2010 Examples 4
Drawing 5 cards from a deck of 52 cards without
ith
replacement
Consider event C = draw a heart
draw
? What is the probability of getting all hearts? NUS/FoS/DSAP 12 GEM2900  Understanding Uncertainty & Statistical Thinking Semester 1, 2009/2010 Examples 5
In
In the game of blackjack, the pictured cards count as 10
the
points and the ace counts as either 1 or 11 points. All other
cards are counted at their face values. Blackjack is achieved
if
if 2 cards total 21 points.
? What is the probability of getting blackjack? NUS/FoS/DSAP 13 GEM2900  Understanding Uncertainty & Statistical Thinking Semester 1, 2009/2010 Examples 6
Is
Is ultrasound a reliable method for determining the gender of an
unborn baby? 1000 births were observed. Ultrasound predicted
562 baby girls and 438 baby boys. Ultrasound has made 130
wrong predictions on baby girls and 48 wrong predictions on
baby boys.
? Use a contingency table to summarize the above information. ultrasound scan
boy
actual
gender NUS/FoS/DSAP girl boy
girl 14 GEM2900  Understanding Uncertainty & Statistical Thinking Semester 1, 2009/2010 Examples 6, (continued)
? What is the probability that the ultrasound will make a wrong
prediction? ? Do you think the ultrasound results are equally reliable in
predicting genders for baby boys and baby girls? NUS/FoS/DSAP 15 GEM2900  Understanding Uncertainty & Statistical Thinking Semester 1, 2009/2010 How to Calculate with
Probabilities (Continued)
Law of Total Probability (simple version)
(si
Consider a sample space, S, can be partitioned into 2
mutually
mutually exclusive events, X and Y
A is an event in sample space S
X A Y A P(A) = P(A ∩ X) + P(A ∩ Y)
= P(A  X) × P(X) + P(A  Y) × P(Y) NUS/FoS/DSAP 16 GEM2900  Understanding Uncertainty & Statistical Thinking Semester 1, 2009/2010 How to Calculate with
Probabilities (Continued) NUS/FoS/DSAP 17 GEM2900  Understanding Uncertainty & Statistical Thinking Semester 1, 2009/2010 How to Calculate with
Probabilities (Continued) Let C = {Catastrophe}
{Catastrophe}
U = {Known physics gives correct calculation} Then P (C ) = P (C ∩ U ) + P (C ∩ U )
= P (C  U ) × P (U ) + P (C  U ) × P (U ) NUS/FoS/DSAP 18 GEM2900  Understanding Uncertainty & Statistical Thinking Semester 1, 2009/2010 How to Calculate with
Probabilities (Continued) NUS/FoS/DSAP 19 GEM2900  Understanding Uncertainty & Statistical Thinking Semester 1, 2009/2010 How to Calculate with
Probabilities (Continued)
Law of Total Probability
√ A sample space S, can be partitioned into 2 mutually
exclusive events, X and Y
P(A) = P(A  X) × P(X) + P(A  Y) × P(Y)
√ A sample space S, can be partitioned into n mutually
exclusive events, X1, X2, …, Xn
P(A) = P(AX1)×P(X1)+P(AX2)×P(X2)+… P(AXn)×P(Xn)
 NUS/FoS/DSAP 20...
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