Question

Sam have 6 denomination of 1 dollars, 5 denomination of 10 dollars and 4 denomination of 5 dollars. 2 denominations are chosen randomly with replacement. Find the probability of drawing 10 dollar followed by 10 dollar?

• A. $\frac{4}{45}$
• B. $\frac{1}{9}$
• C. $\frac{4}{15}$
• D. $\frac{20}{15}$

Answer 1

The correct option is B $\frac{1}{9}$

Given,
Number of 1 dollar denomination $=6$
Number of 10 dollars denomination $=5$
Number of 5 dollars denomination $=4$
Total Number of denomination $=6+5+4=15$

Probability of getting first 10 dollar denomination is $\text{P(A)}=\frac{5}{15}=\frac{1}{3}$

Probability of getting second 10 dollar denomination is $\text{P(B)}=\frac{5}{15}=\frac{1}{3}$

Now, we have to find probablity of getting both $10$ dollar denominations with replacement.

$\Rightarrow \text{P(A and B)}=\text{P(E)}=\text{P(A)}\times \text{P(B)}$

$\Rightarrow \text{P(E)}=\frac{1}{3}\times \frac{1}{3}=\frac{1}{9}$