Question

the distribution of colors of candies in a bag is as follows.

if two candies are randomly drawn from the bag with replacement, what is the probability that they are the same color?
(a) 0.09
(b) 0.22
(c) 0.25
(d) 0.75
(e) 0.78

Explanation:

Step1: Calculate probability for each color

For brown: \(0.3\times0.3 = 0.09\)
For red: \(0.2\times0.2=0.04\)
For yellow: \(0.2\times0.2 = 0.04\)
For green: \(0.2\times0.2=0.04\)
For orange: \(0.1\times0.1 = 0.01\)

Step2: Sum up the probabilities

\(0.09 + 0.04+0.04 + 0.04+0.01=0.22\)

Answer:

B. \(0.22\)