Construct and use a Two-Way Table to solve the following: • A Pap smear is a tes
ID: 3361861 • Letter: C
Question
Construct and use a Two-Way Table to solve the following: • A Pap smear is a test that can detect cervical cancer. • According to a study published in Scientific American, the probability that a woman has cervical cancer is .00008. • The chance that a Pap smear test will incorrectly come back positive, indicating that a woman without cervical cancer has cervical cancer is .03.
a) What is the probability that a randomly chosen woman who has this test (Pap smear) will both be free of cervical cancer and test positive.
b) Give a statement to interpret your answer.
Explanation / Answer
Ans:
From given data:
P(positive/no cancer)=0.03
P(positive and no cancer)/P(no cancer)=0.03
P(no cancer)=1-0.00008=0.99992
P(positive and no cancer)=0.03*0.99992=0.029998
(Note:P(positive/cancer) is required to calculate other entries.)
a)P(negative/no cancer)=1-P(positive/no cancer)=1-0.03=0.97
P(negative and no cancer)=0.97*0.99992=0.969922
b)Probability that a randomly selected women has no cervical cancer and test negative is 0.969922
Cancer No cancer Marginal positive 0.029998 negative 0.969922 Marginal= 0.00008 0.99992