probability please

Question

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 both people have licenses? Write your answer as a fraction in simplest form.

Answer 1

Hi Crystal,

Given information:

1. There are 8  people fishing at Lake Connor: 
2. 3  have fishing licenses 
3. 5  do not.
4. 2 Chosen at random

FIND: What is the probability that both people have licenses? Write your answer as a fraction in simplest form.

These events are dependent. Once you choose 1 person with a license, now there are less people to choose from and there is one less person with a license.

Dependent events A and B, P(A and B)=P(A)×P(B│A)

Dependent events = Probability of A times P(B│A)=probability of B given that A has already occurred

To start with you have 8 people, 3 with license.

Probability of an event = (number of favorable outcomes)/(total number of outcomes)

P(A)= (3/8) for the 1st person with a license

Now there are 7 people left and only 2 with a license.

P(B)= (2/7) for the probability of getting the 2nd person with license.

The total probability is the product of the two probabilities.

P(B|A)=(3/8) x (2/7)

= (6/56)

= 3/28

Hope this helps.

Let me know if you need more clarification :)