# Not able to figure out the favorable vs total outcomes

• Apr 2nd 2011, 12:28 AM
mathguy80
Not able to figure out the favorable vs total outcomes
Hey Guys,

Another probability problem. I am not able to figure out the right values to use for favorable outcomes.

In a medical experiment, some students who suffered from stress were given the drug "StressOff" while others were given "Placebo". The proportions in different categories are given below.

$
\begin{tabular}{ | c |c| c| }
\hline
& StressOff & Placebo \\
\hline
Improved & 0.32 & 0.14\\
Did not improve & 0.26 & p\\
\hline
\end{tabular}
$

1. Find the value of p.
2. Find the probability that a student chosen at random
1. Took the drug "StressOff" but did not improve,
2. did not improve at all
3. improved given that he or she took the drug "Placebo"

(I)
These are percentages so,
$p = 1 - (0.32 + 0.14 + 0.26) = 0.28$

(II-a)
$P(StressOff) = 0.32+0.26 = 0.58$

$P(\textnormal{Did not improve}) = 0.26$

$P(\textnormal{StressOff and Did not improve}) = 0.58 \times 0.26 \approx 0.39$

This is wrong, the required answer is 0.32. When calculating probability of not improve, are the favorable outcomes out of only people part of the StressOff group?

(II-b) $P(\textnormal{Did not improved}) = 0.26 + 0.28 = 0.54$

This is the only thing I have got right in this problem!

(II-c)
$P(Placebo) = 0.14 + 0.28 = 0.42$

$P(Improved) = 0.14$

$P(\textnormal{Placebo and Improved}] = 0.42 \times 0.14 \approx 0.06$

Again incorrect, the required answer is 0.15

Any inputs to help me figure out what I did wrong here would be greatly appreciated. Thanks.
• Apr 2nd 2011, 12:45 AM
CaptainBlack
Quote:

Originally Posted by mathguy80
Hey Guys,

Another probability problem. I am not able to figure out the right values to use for favorable outcomes.

In a medical experiment, some students who suffered from stress were given the drug "StressOff" while others were given "Placebo". The proportions in different categories are given below.

$
\begin{tabular}{ | c |c| c| }
\hline
& StressOff & Placebo \\
\hline
Improved & 0.32 & 0.14\\
Did not improve & 0.26 & p\\
\hline
\end{tabular}
$

1. Find the value of p.
2. Find the probability that a student chosen at random
1. Took the drug "StressOff" but did not improve,
2. did not improve at all
3. improved given that he or she took the drug "Placebo"

II.A is just the content of the cell took SF & DNI = 0.26

II.B Is the sum of the DNI row

II.c We are working with the column P. The required prob is I & P divided by the column total: (0.14)/(0.42)

CB
• Apr 2nd 2011, 01:08 AM
mathguy80
Thanks @CaptainBlack. I guess I was over thinking this one.

Quote:

Originally Posted by CaptainBlack

II.c We are working with the column P. The required prob is I & P divided by the column total: (0.14)/(0.42)

II.c (0.14)/(0.42) = 0.33. The required answer was 0.15. I am thinking like II.a isn't this also a direct value from Placebo and Improved, ie:- 0.14. Can you please clarify a little why II.c should be interpreted differently than II.a?

Thanks.