There are 15 tickets in a box, each bearing one of the numbers from 1 to 15. One ticket is drawn at random from the box. Find the probability of event that the ticket drawn
(1) shows an even number
(2) shows a number which is a multiple of 5.

Answer

(1) `(7)/(15)`
(2) `(1)/(5)`

Explanation

"The sample space is"
`S={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}`
`n(S)=15`
(1) Let A be event that the ticket drawn bears an even number.
`Then,A={2,4,6,8,10,12,14}`
`thereforen(A)=7`
`P(A)=(n(A))/(n(S))=(7)/(15)`
`thereforeP(A)=(7)/(15).`
Let B be the event that the ticket drawn bears a number which is a multiple of 5.
`Then,B={5,10,15}`
`thereforen(B)=3`
`P(B)=(n(B))/(n(S))=(3)/(15)=(1)/(5)`
`thereforeP(B)=(1)/(5).`