# Thread: 2 Q. needs 2 ANS.

1. ## 2 Q. needs 2 ANS.

22. in a city ,25% of the cars emit pollutions to the air of the city .if a car failed to pass the emission of air pollutants with probability 0.99 and if a car that is not emitting air pollutants also fails the test with probability 0.17 .what is the probability that a car that fails the test actually emits air pollution ?

23.the number of employees working in factories A,B and C are , respectively 50,75 and 100 . suppose that of those employees ,50% ,60 % and 70%,respectively ,are women .assuming that the probability of resignation is the same for men and women and that woman resigned ,what is the probability that she is from factory c ?

2. Hello, compufatwa!

I'll do the second one . . .

These are Conditional Probability problems.
You're expected to be familiar with the formula: . $P(A|B) \:=\:\frac{P(A \wedge B)}{P(B)}$

23. The number of employees at factories A,B and C are , respectively 50, 75 and 100.
Suppose that of those employees, 50%, 60% and 70%, respectively, are women.

Assuming that the probability of resignation is the same for men and women
and that woman resigned, what is the probability that she is from factory C?
I tabulated the data . . .

$\begin{array}{cccccccc}
& |& \text{Women} &|& \text{Men} &|& \text{Total} & | \\ \hline
A &|& 25 &|& 25 &|&50 &| \\
B &|& 45 &|& 30 &|&75 &| \\
C &|& 70 &|& 30 &|& 100 &| \\ \hline
\text{Total} &|& 140 &|& 85 &|& 225 &| \end{array}$

Formula: . $P(\text{from C }|\text{ Woman}) \;=\;\frac{P(\text{from C }\wedge\text{ Woman})}{P(\text{Woman})}$

From the chart, we have: . $\begin{Bmatrix}P(\text{from C }\wedge\text{ Woman}) &=& \frac{70}{225} \\
P(\text{Woman}) & = & \frac{140}{225} \end{Bmatrix}$

Therefore: . $P(\text{from C }|\text{ Woman}) \;=\;\frac{\frac{70}{225}}{\frac{140}{225}} \;=\;\frac{1}{2}$

But check my reasoning and work . . . please!
.

3. Soroban thanks alot for the answer