Question

:​ ​choose​ ​the​ ​correct​ ​answer. In​ ​a​ ​purse​ ​there​ ​are​ ​30​ ​coins,​ ​twenty​ ​one-rupee​ ​and​ ​remaining​ ​50-paise​ ​coins.​ ​eleven​ ​coins​ ​are​ ​picked simultaneously​ ​at​ ​random​ ​and​ ​are​ ​placed​ ​in​ ​a​ ​box.​ ​if​ ​a​ ​coin​ ​is​ ​now​ ​picked​ ​from​ ​the​ ​box,​ ​find​ ​the probability​ ​of​ ​it​ ​being​ ​a​ ​rupee​ ​coin? Option​ ​1​ ​:​ ​4/7 option​ ​2​ ​:​ ​1/2 option​ ​3​ ​:​ ​2/3 option​ ​4​ ​:​ ​5/6

Answer 1

$\mathfrak{\huge{\blue{Solution:}}}$

Given,
In a purse,
Total No. of Coins = 30

No. of One Re. coins = 20
No. of 50 ps. coins = 10

Let S be sample space
n(S) - No. of ways of picking a coin from the purse
$n(S) = 30_{C}__{1}$

•°• n(S) = 30

Let E be the Event that the coin picked from purse is a Re. coin
n(E) - No. of Favourable ways to satisfy Event 'E'

^^ If picked one must be a Rupee coin, it must be picked from the total no. of Re. coins
$n(E) = 20_{C}__{1}$

•°• n(E) = 20

Probability of occurrence of Event

$= \frac{No.\: of\: favourable\: outcomes}{No.\: of\: total\: outcomes}$

$P(E) = \frac{n(E)}{n(S)}$

$P(E) = \frac{20}{30} = \frac{2}{3}$

•°• $Required Probability = \frac{2}{3}$

This Answer exists in $\mathcal{\underline{\underline{\pink{Option\: 3}}}}$

$\mathfrak{\huge{\red{Hope\: it\: helps}}}$