Respuesta :
We have been given that a friend has tickets to a concert and who selects 2 of them at random to give to you and we are also told that your friend has 13 tickets of which 5 are in the front row and 8 are in the tenth row.
We are asked to find out probability that both of the tickets you receive are in the front row.
In order to find out the probability that both of the tickets you receive are in the front row we will use probability formula.
[tex]\text{Probability of an event}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}[/tex]
[tex]\text{Possible number of outcomes}=_{2}^{5}\textrm{C}[/tex]
[tex]\frac{5!}{(5-2)!\cdot 2!}=\frac{5!}{3!\cdot 2!}\\=\frac{5\cdot 4\cdot 3!}{3!\cdot 2\cdot 1}=5\cdot 2=10[/tex]
Now let us find out total number of possible outcomes,
[tex]\text{Total number of possible outcomes}=_{2}^{13}\textrm{C}\\=\frac{13!}{(13-2)!\cdot 2!}=\frac{13!}{11!\cdot 2!}\\\frac{13\cdot 12\cdot 11!}{11!\cdot 2\cdot 1}=13\cdot 6=78[/tex]
Now we can find out probability of getting both tickets in the front row by substituting our values in probability formula.
[tex]\text{Probability of getting both seats in front row}=\frac{10}{78}\\=\frac{5}{39}=0.128205[/tex]
