Question

A new medicine was given to a sample of 25 of Dr. Cleary’s patients with flu symptoms. Of the total, 19 patients reacted favorably, 2 reacted unfavorably, and 4 were unaffected. Three of these patients are selected at random. Determine the probability of the following. a) All three reacted favorably.

b) The first patient reacted favorably, the second patient reacted unfavorably, and the third patient was unaffected.

c) No patient reacted favorably.

d) At least one patient reacted favorably.
I have the answers, just I don't understand how they are done. Answers are :
A) = 19/25* 18/24 * 17/23 = 969/2300
B) =19/25 * 2/24 * 4/23 = 19/1725
C= 6/25 *5/24 * 4/23 = 1/115
and D) = I understand.
Thanks in advance

Answer 1

Anybody? Even a slight idea would be helpful.

Answer 2

Find the individual probabilities first
favorably = 19/25
unfavorably = 2/25
unaffected = 4/25

Answer 3

Those are for the first patient selected at random.
The probabilities for the second patient need a denominator of 24 because 1 out of the 25 has already been selected out.

Answer 4

e.g. for (A) = 19/25 * 18/24 * 17/23
19/25 is probability of first selected to be in the 'favorably' category.
18/24 is because 1 out of the favorably category has already been selected out, and there are now 24 total remaining to choose from.
17/23 is for similar reasons.

Is that enough to make sense of the rest?

Answer 5

Okay it's not as confusing as I'd thought. What threw me was the "= 969/2300" I couldn't see where that figure came in to play. Thanks :-)

Answer 6

19/25 * 18/24 * 17/23 = 5814/13800, which reduces to 969/2300.

Answer 7

Okay. thanks I think I understand what's going on with it now, I wasn't reducing the figures and that was my problem, call it a brain malfunction

Answer 8

Brains do that from time to time.