Answer:
[tex]\dfrac{5}{273}[/tex]
They are dependent events.
Step-by-step explanation:
Given:
Number of $1 gift certificates = 2
Number of $2 gift certificates = 2
Number of $3 gift certificates = 10
To find:
Probability that a $1 gift certificate is selected, then a $3 and then a $2 certificate is selected = ?
Solution:
First of all, let us learn about the formula of probability of any event E:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Finding probability of choosing $1 gift certificate in the first turn:
Number of favorable cases or number of $1 gift certificates = 2
Total number of cases or total number gift certificates = 2 + 2 + 10 = 14
So, required probability = [tex]\frac{2}{14} \Rightarrow \frac{1}{7}[/tex]
Finding probability of choosing $3 gift certificate in the 2nd turn:
Number of favorable cases or number of $1 gift certificates = 10
Now, one gift certificate is already chosen,
So, Total number of cases or total number gift certificates = 14 - 1 = 13
So, required probability = [tex]\frac{10}{13}[/tex]
Finding probability of choosing $2 gift certificate in the 3rd turn:
Number of favorable cases or number of $2 gift certificates = 2
Now, two gift certificates is already chosen,
So, Total number of cases or total number gift certificates = 14 - 2 = 12
So, required probability = [tex]\frac{2}{12} \Rightarrow \frac{1}{6}[/tex]
Probability that a $1 gift certificate is selected, then a $3 and then a $2 certificate is selected:
[tex]\dfrac{1}{7}\times \dfrac{10}{13}\times \dfrac{1}{6}\\\Rightarrow \dfrac{5}{273}[/tex]
They are dependent events because total number of cases and total number of favorable cases depend on the previous chosen gift certificate.
So, the answer is:
[tex]\dfrac{5}{273}[/tex]
They are dependent events.
