Question

3.NaturUS produces and distributes natural products. It is currently testing its Rest-E-Z pill

which is meant to provide relief to patients from insomnia and other sleeping disorders. A

sample of 800 patients who suffer from insomnia were submitted to clinical testing. 600

patients were treated with the Rest E-Z pill, while 200 were administered a placebo. 400 of the

patients stated they benefited from their treatment, 320 of which had actually been given Rest-

E-Z. Let us define the events:

R= “the patient was treated with the Rest-E-Z pill”

B= “the patient felt benefits from the treatment”

A)Find the values of i)?(?) ii)?(?) iii)?(? ∩ ?)

B)Find ? ? ? and explain the meaning of this probability in the context of the

problem.

C)Find ?(?|?) and explain the meaning of this probability in the context of the

problem.

D)Are events R and B independent? Justify your answer.

Answer 1

Here we are guven that NaturUS produces and distributes natural products. It is currently testing its Rest-E-Z pill

which is meant to provide relief to patients from insomnia and other sleeping disorders. A

sample of 800 patients who suffer from insomnia were submitted to clinical testing. 600

patients were treated with the Rest E-Z pill, while 200 were administered a placebo. 400 of the

patients stated they benefited from their treatment, 320 of which had actually been given Rest-

E-Z. Let us define the events:

R= “the patient was treated with the Rest-E-Z pill”

B= “the patient felt benefits from the treatment”

A) We have to find the values of:

i) P(R) = 600/800 = 3/4

ii) P(B) = 400/800 = 1/2

iii) = 320/800 = 2/5

B) We have to find P(R|B) = / P(B)

= (2/5) / (1/2)

= 4/5

The meaning of this probability is that the paitent was treated with rest E_Z pill given that the patient felt benefits from the treatment.

iii)

We have to find P(B|R) = / P(R)

= (2/5) / (3/4)

= 8/15

The meaning of this probability is that the patient felt benefits from the treatment given that the paitent was treated with rest E_Z pill.

D) To find that if the events R and B are independent we have to check the following condition that-

Here, P(R)P(B) = 3/4 * 1/2 = 3/8 and

= 2/5

So they are not equal, hence R and B are not independent.