Answer:
[tex]\texttt{Probability of choosing two candies of the same color}=\frac{7}{22}[/tex]
Step-by-step explanation:
Probability of choosing two candies of the same color = Probability of choosing 2 red candies + Probability of choosing 2 yellow candies + Probability of choosing 2 blue candies.
Number of total candies = 15+15+15 = 45
Number of red candies = 15
[tex]\texttt{Probability of choosing 2 red candies}=\frac{15}{45}\times \frac{14}{44}=\frac{1}{3}\times \frac{7}{22}=\frac{7}{66}[/tex]
Number of yellow candies = 15
[tex]\texttt{Probability of choosing 2 yellow candies}=\frac{15}{45}\times \frac{14}{44}=\frac{1}{3}\times \frac{7}{22}=\frac{7}{66}[/tex]
Number of blue candies = 15
[tex]\texttt{Probability of choosing 2 blue candies}=\frac{15}{45}\times \frac{14}{44}=\frac{1}{3}\times \frac{7}{22}=\frac{7}{66}[/tex]
[tex]\texttt{Probability of choosing two candies of the same color}=\frac{7}{66}+\frac{7}{66}+\frac{7}{66}\\\\\texttt{Probability of choosing two candies of the same color}=\frac{7}{22}[/tex]
