6.3 Conditional Probability

 Calculate Conditional Probabilities  Determine if events are independent

 #1) 0 ≤ P(A) ≤ 1  #2) P(S) = 1  #3)  #4) P(A or B)= P(A) + P(B)  #5) P(A and B)= P(A) P(B)

 Joint event- (A and B)  Joint probability- P(A and B)

 P(one or more of A, B, C)= P(A) + P(B) + P(C)

 For any two events A and B, P(A or B)= P(A) + P(B) – P(A and B)

 P(D)=0.7  P(M)=0.5  P(D and M)=0.3 Find a) P(D and Mʿ)= 0.4 b) P(Dʿ and Mʿ)= 0.1

 6.37: P(A or B)= P(A) + P(B) – P(A and B) = – 0.077= : P(A or B)= 0.8

Ex: Pg. 347  P(married)= 58,929/99,585  P(married | age 18 to 24)= 3,046/12,614  P( married and 18 to 24) = 3,046/99,585

 When P(A)>0, the conditional probability of B given A is: P(B | A)= P (A and B) P(A)

 Ex: The probability that Mike has a Visa card is The probability that Mike has a Visa and a Master card is What is the probability that Mike has a Master card given he has a Visa? P(M | V)= P (M and V) = 0.23 = 0.51 P(V) 0.45

Ex: Only 5% of male high school basketball, baseball, and football players go on to play at the college level. Of these, only 1.7% enter major league professional sports. About 40% of the athletes who compete in college and then reach the pros have a career of more than 3 years.  Define these events: C= college after high school M= major league after college 3= 3 or more years of pro

 What is the probability that a high school athlete competes in college and then goes on to have a pro career of more than 3 years?

 Ex: The probability that a doctor is on call is The probability that a doctor performs a surgery is The probability a doctor performs a surgery and he is on call is What is the probability the doctor is performing a surgery given he is on call? P(S | C)= P (S and C) = = 0.34 P(C) 0.15

 Does P(S and C)= P(S) P(C) ?? ≠ 0.15 * ≠ therefore they are NOT independent