Question

Ian gave each of his $2$ buddies a candy at his birthday celebration, with the treats being $2$ Hazel Nut bars, $2$ Coconut Milk bars, and $1$ Dates bars. What is the probability that both of Ian's friends got the same type of candy?

• A. $\frac{1}{5}$
• B. $\frac{2}{5}$
• C. $\frac{1}{10}$
• D. $\frac{4}{5}$

Answer 1

The correct option is A $\frac{1}{5}$

Given that:

Total number of candy $=5$

Number Hazel nut bars $=2$

Number of Coconut milk bars $=2$

Number of Dates milk bar $=1$

So,
ways of seletion of $2$ Hazel nut bars
$={}^2{C}_2=1$

ways of seletion of $2$ Coconut milk bars
$={}^2{C}_2=1$

and ways of selection 2 candy out 5
$={}^5{C}_2=\frac{5\times 4}{2!}=10$

$\Rightarrow$ Probabilty of getting same Hazel nut bars
$=\frac{1}{10}$

$\Rightarrow$ Probabilty of getting same Coconut milk bars
$=\frac{1}{10}$

Hence,
Probability of getting same type of candy $=\frac{1}{10}+\frac{1}{10}$
$=\frac{2}{10}$
$=\frac{1}{5}$

Short cut method
There are $2$ ways he can give same type of candy to both friends either Hazel nut bars or Coconut milk bars.

And there are $10$ ways to select $2$ candies out of $5$.

So,
Probabilty of getting same type of candy $=\frac{2}{10}$
$=\frac{1}{5}$