AP Statistics6.3 Conditional Probability
Calculate Conditional Probabilities
Determine if events are independent
Learning Objective:
#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)
Review:Probability Rules
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)
Addition Rule for Disjoint Events
For any two events A and B,
P(A or B)= P(A) + P(B) – P(A and B)
General Addition Rule for Unions of Two Events
P(D)=0.7 P(M)=0.5 P(D and M)=0.3
Find a) P(D and Mʿ)=
0.4b) P(Dʿ and Mʿ)=
0.1
Venn Diagram
6.37:P(A or B)= P(A) + P(B) – P(A and B)
= 0.125 + 0.237 – 0.077=0.285
6.38:P(A or B)= 0.8
Pg. 345 (Complete with your partner): 6.37-6.40
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
Conditional Probability
When P(A)>0, the conditional probability of
B given A is:
P(B | A)= P (A and B) P(A)
Definition of Conditional Probability:
Ex: The probability that Mike has a Visa card is 0.45. The probability that Mike has a Visa and a Master card is 0.23. 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 schoolM= major league after college
3= 3 or more years of pro
Intersection-
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 0.15. The probability that a doctor performs a surgery is 0.24. The probability a doctor performs a surgery and he is on call is 0.051. What is the probability the doctor is performing a surgery given he is on call?
P(S | C)= P (S and C) = 0.051 = 0.34 P(C) 0.15
Independent Events:
Does P(S and C)= P(S) P(C) ??
0. 051 ≠ 0.15 * 0 .240.051 ≠ 0.036
therefore they are NOT independent
Are they independent?