Question

A box contains 25 notes, $1rs.$ is marked on 19 notes of them and $5rs.$ on remaining notes. Another box B contains 50 notes in it $1rs.$ is marked on 45 notes of them and $13rs.$ is marked on the remaining notes. All the noted of two given boxes are collected and put them into another box and mixed them properly. A note is at random drawn from this box. What is the probability that the note drawn has some thing else beside $1rs.$

Answer 1

1) Box A-

Total number of notes = $25$

Number of $1rs.$ notes = $19$

Number of notes other than $1rs.$ notes = $25-19=6$

2) Box B-

Total number of notes = $50$

Number of $1rs.$ notes = $45$

Number of notes other than $1rs.$ notes = $50-45=5$

When notes in both the boxes are mixed in a separate box,

Total number of notes = $25+50=75$

Total number of $1rs.notes$ = $19+45=64$

Number of notes other than $1rs.$ notes = $6+5=11$

Let $A$ = Event such that note drawn at random is note other than $1rs.$ note

$n\left(A\right)=11$

$n\left(S\right)=75$

$\therefore P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}$

$\therefore P\left(A\right)=\frac{11}{75}$