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.

$\displaystyle

\begin{tabular}{ | c |c| c| }

\hline

& StressOff & Placebo \\

\hline

Improved & 0.32 & 0.14\\

Did not improve & 0.26 & p\\

\hline

\end{tabular}

$

- Find the value of p.
- Find the probability that a student chosen at random

- Took the drug "StressOff" but did not improve,
- did not improve at all
- improved given that he or she took the drug "Placebo"

(I)

These are percentages so,

$\displaystyle p = 1 - (0.32 + 0.14 + 0.26) = 0.28$

(II-a)

$\displaystyle P(StressOff) = 0.32+0.26 = 0.58$

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

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

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

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

(II-c)

$\displaystyle P(Placebo) = 0.14 + 0.28 = 0.42$

$\displaystyle P(Improved) = 0.14$

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

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.