# probability with teen pregnancy

• Apr 25th 2008, 03:06 AM
gbgb
probability with teen pregnancy
heres the question.
What is the conditional probability that a teenage pregnancy is in a young mother 15 to 17 years old, given that she is classified as white ? what is the conditional probability that a teenage pregnancy is in a young mother 15 to 17 years old, given that she classified as black.

heres the chart
-----------------15 to 17 -----------------18 to 19
white--------------23------------------------.49
black--------------.09-----------------------.15
other--------------.01-----------------------.03

THANKSS!! any help would be helpful!
• Apr 25th 2008, 03:52 AM
janvdl
Quote:

Originally Posted by gbgb
heres the question.
What is the conditional probability that a teenage pregnancy is in a young mother 15 to 17 years old, given that she is classified as white ? what is the conditional probability that a teenage pregnancy is in a young mother 15 to 17 years old, given that she classified as black.

heres the chart
-----------------15 to 17 -----------------18 to 19
white--------------23------------------------.49
black--------------.09-----------------------.15
other--------------.01-----------------------.03

THANKSS!! any help would be helpful!

Use Bayes' Rule.

For white:

$\displaystyle P(15-17 | W) = \frac{P(W | 15-17)P(15-17)}{P(W | 15-17)P(15-17) + P(W | 18-19)P(18-19)}$

$\displaystyle = \frac{(.23)(.33)}{(.23)(.33) + (.49)(.67)}$

For black:

$\displaystyle P(15-17 | B) = \frac{P(B | 15-17)P(15-17)}{P(B | 15-17)P(15-17) + P(B | 18-19)P(18-19)}$

$\displaystyle = \frac{(.09)(.33)}{(.09)(.33) + (.15)(.67)}$
• Apr 25th 2008, 06:33 AM
CaptainBlack
Quote:

Originally Posted by gbgb
heres the question.
What is the conditional probability that a teenage pregnancy is in a young mother 15 to 17 years old, given that she is classified as white ?

23/(23+49)~=0.319

Explanation: in a sample of 100 teen pregnancies 72 are white, and of those 23 are "15 to 17"'s (on average)

RonL