Question

A bag contains 6 Red, 5 Blue and 4 Green balls. If two balls are drawn at random what is the probability that both
are of same color?​

Answer 1

Answer:

2/15 is the probability of the balls

Answer 2

Answer:

The probability that both are of same color is equal to 1/3 when two balls are drawn at random.

Step-by-step explanation:

The total number of balls $=6+5+4=15$

Number of ways selecting two balls out of 15 balls:

$^{15}C_{2}=\frac{15!}{2!(15-2)!}=\frac{15!}{2!*13!} =105$

Number of red balls =6

The number of ways selecting two red balls $=^{6}C_{2}=\frac{6!}{2!*4!}=15$

Number of Blue balls =5

The number of ways selecting two Blue  balls $=^{5}C_{2}=\frac{5!}{2!*3!}=10$

Number of green balls =4

The number of ways selecting two green balls $=^{4}C_{2}=\frac{4!}{2!*2!} =6$

$Probability=\frac{No. \; of \;possible\; outcomes}{Total \; no. \; of \; outcomes}$

Probability that both are of same color:

$P(E)=\frac{^{6}C_{2}+^{5}C_{2}+^{4}C_{2}}{^{15}C_{2}}$

$P(E)=\frac{15+10+6}{105}$

$P(E)=\frac{35}{105}$

$P(E)=\frac{1}{3}$

Therefore, when two balls are drawn randomly, the probability that both are of same color is 1/3.