Question

A study was performed to determine whether patients experienced an adverse event within two weeks when placed on a particular new medication. The results were as follows:

	Adverse event	No adverse event	Total
Treatment group	109	543	652
Control group	51	290	341
Total	341	652	993

How many people were studied altogether?

If a patient is selected at random from among those studied, what is the probability that that person was in the control group? Round your answer to two decimal places.

If a patient is selected at random from among those studied, what is the probability that that person was in the treatment group and experienced an adverse event? Round your answer to two decimal places.

If a patient is selected at random from among those studied, what is the probability that that person was in the treatment group, given that the person experienced an adverse event? Round your answer to two decimal places.

What is the sample space for this experiment?

A. 109, 51, 543, 290
B. Treatment group, Control group, Adverse event, No adverse event
C. 993
D. Treatment group/Adverse event, Treatment group/No adverse event, Control group/Adverse event, Control group/No adverse event

Are the events “Treatment group” and “Adverse event” independent?

A. No
B. Yes

Answer 1

(a)

Number of people were studied altogether = 993

(b)

If a patient is selected at random from among those studied, the probability that that person was in the control group = 341/993 = 0.34

(c)

If a patient is selected at random from among those studied, the probability that that person was in the treatment group and experienced an adverse event = 109/993 = 0.11

(d)

If a patient is selected at random from among those studied, the probability that that person was in the treatment group, given that the person experienced an adverse event = P(Treatment group/ Adverse event) = P(Treatment group AND Adverse event) / P(Adverse event)

= 109/341 = 0.32

(e)

the sample space for this experiment

Correct option:

D. Treatment group/Adverse event, Treatment group/No adverse event, Control group/Adverse event, Control group/No adverse event

(f)

Correct option:

A.   No

Explanation:

P(Treatment group) = 652/993 = 0.6566

P(Adverse event) = 341/993 = 0.3434

So,

P(Treatment group) X P(Adverse event) = 0.6566 X 0.3434 = 0.2255

But,

P(Treatment group AND Adverse event) = 109/993 = 0.1098

Since P(Treatment group) X P(Adverse event) = 0.2255 P(Treatment group AND Adverse event) = 0.1098, the events “Treatment group” and “Adverse event” are not independent.