there are 8 people fishing at lake connor: 3 have fishing licenses, and 5 do not. an inspector chooses two…

there are 8 people fishing at lake connor: 3 have fishing licenses, and 5 do not. an inspector chooses two of the people at random. what is the probability that the first person chosen does not have a license and the second one does? write your answer as a fraction in simplest form.

there are 8 people fishing at lake connor: 3 have fishing licenses, and 5 do not. an inspector chooses two of the people at random. what is the probability that the first person chosen does not have a license and the second one does? write your answer as a fraction in simplest form.

Answer

Explanation:

Step1: Calculate probability of first - no license

The probability that the first person chosen does not have a license is the number of people without a license divided by the total number of people. There are 5 people without a license and 8 people in total. So the probability $P_1=\frac{5}{8}$.

Step2: Calculate probability of second - has license

After one person without a license is chosen, there are 7 people left, and 3 people with a license. So the probability that the second person has a license given that the first person did not have a license is $P_2 = \frac{3}{7}$.

Step3: Calculate the joint probability

Since these are dependent events, the probability that the first person does not have a license and the second one does is the product of the two probabilities. So $P = P_1\times P_2=\frac{5}{8}\times\frac{3}{7}=\frac{15}{56}$.

Answer:

$\frac{15}{56}$