Respuesta :
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)
[tex]P(A)=\frac{favorable\text{ }cases}{total\text{ cases}}=\frac{10}{24}[/tex]- 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
[tex]P(B\text{ after }A)=\frac{9}{23}[/tex]Finally, replacing in the initial formula
[tex]P(A\text{ and }B)=\frac{10}{24}\cdot\frac{9}{23}=\frac{90}{552}=0.1630[/tex]Finally, the probability would be 0.1630
ANSWER:
P (both are letters) = 0.1630
