there are 8 people fishing at lake connor: 5 have fishing licenses, and 3 do not. an inspector chooses two of the people at randon. what is the probability that the first person chosen does noy have a license and the second one does?

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Mathematics

26 January, 07:19

there are 8 people fishing at lake connor: 5 have fishing licenses, and 3 do not. an inspector chooses two of the people at randon. what is the probability that the first person chosen does noy have a license and the second one does?

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Alissa Murphy · Answer 1

3 have a license, 5 do not have a license

the first choice is 5 out of 8, or 5/8

the second choice is 4 out of 7, or 4/7

(5/8) * (4/7) = 20/56=10/28=5/14

another way to look at it is ...

how many ways can you choose 2 people out of 8 people?

8!/2! (8-2) !=8!/2!*6!=8*7/2=56/2=28 ways

how many ways can you choose 2 people out of 5 people?

5!/2! (5-2) !=5!/2!*3!=5*4/2=20/2=10

10/28=5/14 again

call the 5 people who don't have a license A, B, C, D, and E

how can they be paired together?

AB, AC, AD, AE, BC, BD, BE, CD, CE, and DE for a total of 10

again 10/28=5/14