Question

Consider the following data for the patients taking the drug (Ascorbic Acid).

	Placebo	Drug	Sum
Cold	36	87	123
NoCold	224	333	557
Sum	260	420	680

What is the probability that a patient has No Cold? Is this a marginal or joint probability?

a) 0.18 marginal

b) 0.62 marginal

c) 0.82 marginal

d) 0.82 joint

e) 0.86 joint

Question 15

What is the probability that a patient is taking Placebo and has No Cold? Is this a marginal or joint probability?

a) 0.86 joint

b) 0.33 joint

c) 0.33 marginal

d) 0.82 marginal

e) 0.82 joint

Question 16

What is the probability that a patient is taking Placebo or has No Cold and identify the correct formula for this kind of probability?

a) 0.92 F5c

b) 0.87 F5a

c) 0.33 F5c

d) 0.92 F5b

e) 0.87 F5b

Question 17

Find conditional probability P(No Cold | taking the drug), P(No Cold | taking Placebo), P(taking drug | No Cold) and identify the correct formula for this kind of probability?

a) 0.49, 0.33, 0.82 F5ef

b) 0.18, 0.62, 0.82 F5c

c) 0.6, 0.71, 0.79, F5ef

d) 0.79, 0.86, 0.6 F5g

e) 0.79, 0.86, 0.6 F5ef

Question 18

Based on answers to previous questions the row and column variables are ________ (a) independent (b) dependent (c) marginal (d) conditional (e) joint

a) marginal

b) joint

c) dependent

d) independent

e) conditional

Answer 1

	Placebo	Drug	Sum
Cold	36	87	123
No Cold	224	333	557
Sum	260	420	680

The probabilities are

	Placebo	Drug	Sum
Cold	36/680 = 0.052	87/680 = 0.127	123/680 = 0.181
No Cold	224/680 = 0.329	333/680 = 0.489	557/680 = 0.819
Sum	260/680 = 0.382	420/680 = 0.618	680

The probabilities with sum are called as Marginal Probabilities which are maked in blue and the probabilties for individuals like cold, no cold, placebo, drug are called joint probabilities which are marked in orange

Question

The probability that a patient has No Cold is 557/680

= 819 = 0.82 rounded to two decimals

This is a marginal probability

So Answer is C

Question (15)

The probability that a patient istaking placebo and has No Cold is 224/680

= 0.329 = 0.33 rounded to two decimals

This is a joint probability

So Answer is B

Question (16)

The probability that a patient is taking Placebo or has No Cold

Consider Placebo be Pl and No Cold be NC

Here we need P(Pl NC) = P(Pl) + P(NC) - P(Pl NC) which is the correct formula

P(PI) = 0.382 , P(NC) = 0.819, P(Pl NC) = 0.329

P(Pl NC) = 0.382 + 0.819 - 0.329

= 0.872 = 0.87 rounded to two decimals

I havr already given the formula. Could you please specify the format given in the answers for the formaul so i can explain you more

Question (17)

Conditional probability P(No Cold | taking the drug), P(No Cold | taking Placebo), P(taking drug | No Cold)

P(No Cold | taking the drug) = P(No Cold taking the drug) / P (taking the drug)

The formual for P(A | B ) = P(AB) / P(B)

P(No Cold | taking the drug = 0.489 / 0.618

= 0.791 = 0.79 rounded to two decimals

P(No Cold | taking placebo) = P(No Cold taking placebo) / P (placebo)

= 0.329 / 0.382

= 0.861 = 0.86 rounded to two decimals

P(taking drug | No Cold) = P(taking drug No cold) / P (No cold)

= 0.489 / 0.819

= 0.597 = 0.6 rounded to two decimals

I havr already given the formula. Could you please specify the format given in the answers for the formaul so i can explain you more

Question (18)

For two variables A,B to be independent P(AB) shpuld be equal to P(A) * P(B)

If we take one raw variable as Cold and one column variable as Drug

P(Cold Drug ) = 0.127

P(Cold) = 0.181

P(Drug) = 0.618

P(Cold) * P(Drug) = 0.181 * 0.618

= 0.112

Since P(Cold Drug ) is not equal to P(Cold) * P(drug) they are not independent so they should be dependent.

So the Answer is C

The Probability of Drug changes on whether they have cold or not, so they are dependent

Likewise all other row and column variables are dependent on each other