GATE CSE 2017 Set 2 | Question: GA-5

Question

There are $3$ red socks, $4$ green socks and $3$ blue socks.You choose $2$ socks. The probability that they are of the same colour is

• A. $\dfrac{1}{5}$
   
• B. $\dfrac{7}{30}$
   
• C. $\dfrac{1}{4}$
   
• D. $\dfrac{4}{15}$

Answer 1

$\large\dfrac{^{3}C_{2}+^{4}C_{2}+^{3}C_{2}}{^{10}C_{2}}=\dfrac{4}{15}.$

assuming ball are not identical

Correct Answer: $D$

Comments

I thought of using this approach but I stuck at thinking whether or not it is valid to apply combination here !

We apply nCr When n is distinct but here it is group and within the group,the balls are distinct ( assuming)

 

How can we apply nCr then ?

Answer 2

P(Socks of Same Colour) = 2 Red or 2 Green or 2 Blue
$
P(socks of Same Colour) = \frac{3}{10}*\frac{2}{9}+\frac{4}{10}*\frac{3}{9}+\frac{3}{10}*\frac{2}{9}\\

P(socks of Same Colour) = \frac{4}{15}

$

Answer 3

3 different kind of socks so choose 4 socks gives you pair of same color. so 4/15

Answer is d

Comments

gud approch .. but why is there 15 in denominator ?

Answer 4

Probability of selecting two socks of same colour = (3C2+4C2+3C2)/10C2=4/15

Ans: D) 4/15