Discrete Mathematical Structures by Pearson

Combinatorics 5-39

passing through on his way to work. What is the probability that he passed through radar

trap located at L

4

?

Solution: Let L

1

, L

2

, L

3

, and L

4

denotes the events of passing through its location L

1

, L

2

, L

3

, and

L

4

, respectively. Let S denote the event of receiving a speeding ticket. Then

þL þL þL þL

1234

543

()

==

()

==

()

==

()

=

50

100

0

40

100

0

30

100

0

20

10

., ., .,

00

0= .2, and

þ(S/L

1

) = 0.3, þ(S/L

2

) = 0.2, þ(S/L

3

) = 0.4, þ(S/L

4

) = 0.1

Required probability =

þL S

þL þSL

þL þSL

ii

i

4

4

=1

4

()

()()

()

()

∑

=

4

=

×

×+×+

×+×

=

++

02 01

05 03 04 02 03 04 02

01

002

015008 012

..

........

.

...++

==

=

002

002

037

2

37

0 054

.

.

.

.

5.12 CONCEPT OF A RANDOM VARIABLE

If we toss two coins together, ...