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 |
79 |
29 |
| New medication |
23 |
69 |
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). |
a) The probability that the patient showed improvement is
computed here as:
= Total patients who show improvement / Total patient size
= (29 + 69)/200
= 0.49
Therefore 0.49 is the required probability here.
b) The probability that the patient showed improvement, given that he took the new medication is computed using Bayes theorem as:
P( improvement | new medication) = n(improvement and new medication)/ n(new medication)
= 69 / (69 + 23)
= 69/92
= 0.75
Therefore 0.75 is the required probability here.
c) Clearly given that the patient takes new medication, the probability of improvement as in part b) is greater than the probability of improvement in a randomly selected patient. Therefore Yes, because the probability found in part (b) is much greater than the probability found in part (a) is the correct answer here.
Get Answers For Free
Most questions answered within 1 hours.