Question

Probability of dependent eventsThere are 8 people fishing at Lake Connor: 5 have fishing licenses, and 3 do not. An Inspector chooses two of the people at random. What is the probability that neither person has a license? Write your answer as a fraction in simplest form.

Answer 1

Answer:

Probability that neither of the two persons has a license = 3/28

Step-by-step explanation:

Total number of people fishing, n(Total) = 8

Number of people with fishing licenses, n(License) = 5

Number of people without fishing license, n(No license) = 3

Number of ways of choosing 2 people out of 8

`\begin{gathered} 8C2=(8!)/((8-2)!2!) \\ 8C2\text{ = }(8!)/(6!2!) \\ 8C2=(8*7*6!)/(6!*2*1) \\ 8C2=28\text{ ways} \end{gathered}`

Since neither of the two people chosen has a license, they will be chosen from the 3 people who do not have a license

`\begin{gathered} 3C2=(3!)/((3-2)!2!) \\ 3C2=(3*2*1)/(2*1) \\ 3C2=3\text{ ways} \end{gathered}`

Probability that neither of the two persons has a license = 3/28