Question

Tickets numbered from 1 to 30 are mixed up and then a ticket is drawn at random.what is the probability that the drawn ticket has a number which is divisible by 2 and 6?

Answer 1

let E be the Event of drawing ticket with ticket no. as a multiple of 2 or 6
and S be sample space

n(s) = no. of ways of drawing one ticket from 30 tickets
n(S)= 30C1= 30

n(E) = no. of ways of drawing ticket with ticket no. as a multiple of 2 or 6

But since 6= 2*3
All the factors of 6 are also multiple of 2
i.e., No. divided by 6 will always be divided by 2

so
n(E) = no. of ways of drawing ticket with ticket no. as a multiple of 6.

possible cases:
6
12
18
24
30
n(E) = 5

Required probability = n(E)/n(S)
=5/30= 1/6



;)
hope it helps