INFORMATION:
We know that:
- stack of mail consists of 8 bills, 10 letters, and 6 advertisements.
- One piece of mail is drawn at random and put aside. Then a second piece of mail is drawn.
And we must find P (both are letters)
STEP BY STEP EXPLANATION:
To find the probability, we need to know that we have two events. First, when one piece of mail is drawn at random and put aside and, second, when a second piece of mail is drawn.
These two events are dependent. If A and B are dependent events, P(A and B) = P(A) • P(B after A) where P(B after A) is the probability that B occurs after A has occurred.
So, first
- Probability of A (the first piece is letter)
![P(A)=\frac{favorable\text{ }cases}{total\text{ cases}}=\frac{10}{24}](https://tex.z-dn.net/?f=P%28A%29%3D%5Cfrac%7Bfavorable%5Ctext%7B%20%7Dcases%7D%7Btotal%5Ctext%7B%20cases%7D%7D%3D%5Cfrac%7B10%7D%7B24%7D)
- Probability of B after A
Since A already occurred and one piece of the mail was drawn (a letter), now in total we would have 9 letter and 23 total pieces
![P(B\text{ after }A)=\frac{9}{23}](https://tex.z-dn.net/?f=P%28B%5Ctext%7B%20after%20%7DA%29%3D%5Cfrac%7B9%7D%7B23%7D)
Finally, replacing in the initial formula
![P(A\text{ and }B)=\frac{10}{24}\cdot\frac{9}{23}=\frac{90}{552}=0.1630](https://tex.z-dn.net/?f=P%28A%5Ctext%7B%20and%20%7DB%29%3D%5Cfrac%7B10%7D%7B24%7D%5Ccdot%5Cfrac%7B9%7D%7B23%7D%3D%5Cfrac%7B90%7D%7B552%7D%3D0.1630)
Finally, the probability would be 0.1630
ANSWER:
P (both are letters) = 0.1630