Question

Use the data in the accompanying table that summarizes results from a clinical trial of a drug. Let A = Drug Treatment, B = Placebo

	headache	No Headache	total
Drug Treatment (A)	122	585	707
Placebo ( B)	28	672	700
Total	150	1257	1407

Answer the following:

1. Find the probability that patient under treatment p(A)

2. Find p(B)

3. Find the probability a patient has a headache

4. Find the probability a patient has a headache and he is under treatment

5. Find p(the patient have a headache given that he is under drug treatment).

6.  Find p(the patient under treatment given that he has a headache).

Answer 1

1. Probability that patient is under treatment

= P(A)

=

= 707/1407

= 0.5025

.

2. Probability that patient is under placebo

= P(B)

=

= 700/1407

= 0.4975

.

3. Probability that a patient has a headache

= P(H)

=

= 150/1407

= 0.1066

.

4. Probability that a patient has a headache and he is under treatment

= P(A ∩ H) [H stands for a patient having headache]

=

= 122/1407

= 0.0867

.

5. P(The patient has a headache given that he is under drug treatment)

= P(H | A)

= P(H ∩ A)/P(A)

= (122/1407)/(707/1407)

= 0.1726

.

6. P(The patient under treatment given that he has a headache)

= P(A | H)

= P(A ∩ H)/P(H)

= (122/1407)/(150/1407)

= 0.8133

.