Question

A bag contains 15 15 red candies, 15 15 yellow candies, and 15 15 blue candies. what is the probability of randomly choosing two candies of the same color, without replacement?

Answer 1

Based on my calculations, this would be 10%.

Answer 2

`\texttt{Probability of choosing two candies of the same color}=(7)/(22)`

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

`\texttt{Probability of choosing 2 red candies}=(15)/(45)* (14)/(44)=(1)/(3)* (7)/(22)=(7)/(66)`

Number of yellow candies = 15

`\texttt{Probability of choosing 2 yellow candies}=(15)/(45)* (14)/(44)=(1)/(3)* (7)/(22)=(7)/(66)`

Number of blue candies = 15

`\texttt{Probability of choosing 2 blue candies}=(15)/(45)* (14)/(44)=(1)/(3)* (7)/(22)=(7)/(66)`

`\texttt{Probability of choosing two candies of the same color}=(7)/(66)+(7)/(66)+(7)/(66)\\\\\texttt{Probability of choosing two candies of the same color}=(7)/(22)`