draw an ace c draw a heart are events a c independent

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Unformatted text preview: ace 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(A|X1)×P(X1)+P(A|X2)×P(X2)+… P(A|Xn)×P(Xn) | NUS/FoS/DSAP 20...
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