If a program is selected at random, the probability it is infected with a virus is?

Question

A computer store has 10 copies of a word processing program, 12 copies of a spread sheet program and 8 copies of a draw program. Three of the word processing, four of the spread sheet and two of the draw programs are infected with a computer virus.

Answer 1

Total number of programs in a store = 10 + 12 + 8 = 30

Number ways in which one program can be drawn out of 30 programs = 30C₁ 

p(t) = 30

Total number of virus effected programs = 3 + 4 + 2 = 9

Number of favorable events = number of ways in which 1 program infected with virus is selected from 9 infected programs = 9C₁

p(f) = 9

Probability of favorable events is = (Number of favorable events)/(Total number of events)

Probability P(E) = p(f)/p(t)

= 9/30 

P(E) = 3/10.