Question

A bag of coins contain $2$ quarters, $3$ dimes and $4$ pennies probability drawing a dime and then quarter without replacements.

Answer 1

Step-1: Finding the probability of drawing a dime:

There are total $2$ quarters, $3$ dimes and $4$ pennies which is equal to $9$
Probability of first drawing a dime $=\frac{3}{9}$
$=\frac{1}{3}$

Step-2: Finding the probability of drawing a quarter:

There are total $2$ quarters, $2$ dimes and $4$ pennies which is equal to $8$because we already drew a dime without replacement.
Probability of drawing a quarter $=\frac{2}{8}$
$=\frac{1}{4}$

Step-3: Finding the probability of drawing a dime and a quarter without replacement:

Probability of first drawing a dime $=\frac{1}{3}$
Probability of drawing a quarter $=\frac{1}{4}$

probability of drawing a dime and a quarter without replacement $=\frac{1}{3}\times \frac{1}{4}$
$=\frac{1}{12}$

Hence, the required probability is $\frac{1}{12}$.