Respuesta :
Solution:
The total number of sample space is
[tex]n(S)=8[/tex]The number of people with fishing licenses is
[tex]n(L)=4[/tex]The number of people without a fishing license is
[tex]n(W)=4[/tex]Step 1:
We will find the probability of picking the first person without a license, we will have
[tex]Pr(W)=\frac{n(W)}{n(S)}[/tex]by substituting the values, we will have
[tex]\begin{gathered} Pr(W)=\frac{n(W)}{n(S)} \\ Pr(W_1)=\frac{4}{8}=\frac{1}{2} \end{gathered}[/tex]Step 2:
We will find the probability of picking the second person without a license,
Note:
There are 7 people left and 3 of them have a license left as we have picked one in step one
Hence,
The probability will be
[tex]\begin{gathered} Pr(W_2)=\frac{n(W_2)}{7} \\ Pr(W_2)=\frac{3}{7} \end{gathered}[/tex]Step 3:
The probability of choosing two people without a license will be
[tex]Pr(W_1W_2)=Pr(W_1)\times Pr(W_2)[/tex]By substituting the values, we will have
[tex]\begin{gathered} Pr(W_1W_2)=Pr(W_1)\times Pr(W_2) \\ Pr(W_1W_2)=\frac{1}{2}\times\frac{3}{7}=\frac{3}{14} \end{gathered}[/tex]Hence,
The final answer = 3/14
