Question

A group of

200

patients tested a new medication.
Some tried the new medication, and the rest took the old medication.

The results are reported in the following two-way frequency table.

	No improvement	Improvement
Old medication	73	37
New medication	63	27

A patient is chosen at random from this group.

Complete the following. Write your answers as decimals.

(a)Find the probability that the patient showed improvement.

=P(improvement)

(b)Find the probability that the patient showed improvement, given that he took the new medication.

=P(improvement | new medication)

(c)Is there evidence that a patient who takes the new medication is more likely to show improvement than a randomly chosen patient from the group?

Yes, because the probability found in part (b) is much greater than the probability found in part (a).

No, because the probability found in part (b) is much greater than the probability found in part (a).

Yes, because the probability found in part (a) is much greater than the probability found in part (b).

No, because the probability found in part (a) is much greater than the probability found in part (b).

Yes, because the probability found in part (b) is about the same as the probability found in part (a).

No, because the probability found in part (b) is about the same as the probability found in part (a).

Answer 1

The tabulated data is given as

	No improvement	Improvement	TOTAL
Old medication	73	37	110
New medication	63	27	90
TOTAL	136	64	200

(a) Find the probability that the patient showed improvement.

P(improvement)= 64/200

= 0.32

(b) Find the probability that the patient showed improvement, given that he took the new medication.

=0.3

(c)Is there evidence that a patient who takes the new medication is more likely to show improvement than a randomly chosen patient from the group?

No, because the probability found in part (b) is about the same as the probability found in part (a)