Sorry about the lateness of this question. I was a bit distracted this morning.

A doctor knows that the drug he is prescribing is about 30% effective. He currently has four patients on the drug coming in during the next week. He's hoping to hear positive results for three out of the four.

What are the chances that his hopes will be met?

BTW, Did you notice the SocialVibe widget on the sidebar? Please, if you have time, give it a whirl. And then give me some feedback on how it works, what you think of it, etc... Good or bad, I want to know

## Thursday, September 03, 2009

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The SocialVibe thing doesn't work for me. Clicked on it, a popup showed with a question which character are you, so I picked a random character. Then, what was supposed to be the next page suddenly turned out not to be, it hung.

ReplyDeleteThe answer? My guess is 3/10

My guess is a 2.7 % chance.

ReplyDeleteThis is based on the two possible outcomes that meet his criteria.

Probability of 3 patients recovering and one not recovering + probability of all 4 patients recovering.

p(3,1) + p(4,0)

[(30/100)(30/100)(30/100)(70/100)] + [(30/100)(30/100)(30/100)(30/100)] = 0.027

Since he want to hear positive results for 3 out of 4,

ReplyDeleteI would say the probability will be 27/1000 i.e 2.7%

www.guessthelogo.blogspot.comAs Jolson and techie pointed out, the answer is very low. I won't re-explain it, but 2.7% is the answer.

ReplyDeleteYagami, Thanks for trying the widget. I tried it this morning and had the same problem. Hopefully they get it straightened out.

ReplyDeleteMike, I think the chances are higher than that. There are four ways for 3 out of 4 patients to have positive results (P=Positive, N=Negative: NPPP, PNPP, PPNP, PPPN) and one way for 4 patients to have positive results. Therefore the probability that at *least* 3 out of 4 patients have positive results is:

ReplyDelete(4)(3/10)(3/10)(3/10)(7/10) + (1)(3/10)^4

756/10000 + 81/10000 = 837/10000 = 8.37%

Edmund,

ReplyDeleteOops... Last week definitely wasn't my week. You're right. The chances of 3 out of the 4 patients getting positive results is 8.37%. Still depressingly low, but a lot higher than my original answer.

The 16 possibilities are:

PPPP

PPPN

PPNP

PNPP

NPPP

PPNN

PNPN

NPPN

PNNP

NPNP

NNPP

PNNN

NPNN

NNPN

NNNP

NNNN

The four results where 3 out of 4 are positive are as you stated and the chances add up to 8.37%.

Thanks for the correction!