Commute to Work Two-Way Frequency Table Female Male Total

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Presentation transcript:

Commute to Work Two-Way Frequency Table Female Male Total Female Male Total Drive to work 20 40 Walk to Work 50 .6 .5 .4 .7 P(Drive)= P(Male)= P(Drive and Male)= P(Drive or Male)=

Two-Way Frequency Table P(female or Alabama) Female Male Total Alabama 15 5 20 Georgia 55 25 80 70 30 100 P(F) P(A) P(F and A) P(F or A) 70% 20% 15% 75%

3-3 Conditional Probability

𝑃(𝐴|𝐵) Conditional Probability Means: Probability that event A occurs knowing B has already happened Read as “Probability of A given B”

𝑃(𝑅𝑒𝑑|𝐿𝑎𝑟𝑔𝑒) Conditional Probability if you know its large? 50 marbles are in a bag. What is the probability of choosing a red marble if you know its large? Red given large 𝑃(𝑅𝑒𝑑|𝐿𝑎𝑟𝑔𝑒) Red Blue Total Large 12 13 25 Small 8 17 20 30 50

𝑃(𝑠𝑚𝑎𝑙𝑙|𝑏𝑙𝑢𝑒) Conditional Probability 50 marbles are in a bag. What is the probability of choosing a small marble given it’s blue? Red Blue Total Large 12 13 25 Small 8 17 20 30 50 𝑃(𝑠𝑚𝑎𝑙𝑙|𝑏𝑙𝑢𝑒)

Conditional Probability Data on passenger survival on the Titanic. Did being in 1st class increase chances of survival? Strategy: Compare all survivors to survivors in 1st class only. Same % ? Then Independent “No Effect on survival” Different % ? Then Dependent “yes, had an effect on survival” Survived Did Not Survive Total 1st Class 203 122 325 2nd Class 118 167 285 3rd Class 178 528 706 499 817 1316 The casualty figures listed above are from Lord Mersey's Report (British Parliamentary Papers, Shipping Casualties (Loss of the Steamship "Titanic"), 1912 Crew 212 survived out of 908

Conditional Probability Data on passenger survival on the Titanic. Did being in 1st class increase chances of survival? 𝑃(𝑠𝑢𝑟𝑣𝑖𝑣𝑒) Survived Did Not Survive Total 1st Class 203 122 325 2nd Class 118 167 285 3rd Class 178 528 706 499 817 1316 𝑃(𝑠𝑢𝑟𝑣𝑖𝑣𝑒|1𝑠𝑡 𝑐𝑙𝑎𝑠𝑠) Yes, Survival rates depended on which class the passenger was in. 62.5% 37.9% The casualty figures listed above are from Lord Mersey's Report (British Parliamentary Papers, Shipping Casualties (Loss of the Steamship "Titanic"), 1912 Crew 212 survived out of 908.