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?