In: Statistics and Probability
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).
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
.