Final answer:
The given data represents a probability distribution for a discrete random variable. To find the probability of landing on an even number or a multiple of three, we sum up the probabilities of the relevant outcomes.
Step-by-step explanation:
Probability Calculation
The given data represents a probability distribution for a discrete random variable with two possible outcomes: (0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,1), (2,2). The numbers in parentheses represent the possible values the random variable can take. Each value has an associated probability.
For example, P(0,0) is the probability of the random variable taking the value (0,0), which is 0.4. Similarly, P(1,2) is the probability of the random variable taking the value (1,2), which is 0.
To find the probability of landing on an even number or a multiple of three, we need to sum up the probabilities of all the outcomes that satisfy this condition. In this case, the outcomes with even numbers or multiples of three are: (0,0), (0,2), (1,0), (2,0), and (2,2).
P(even or multiple of three) = P(0,0) + P(0,2) + P(1,0) + P(2,0) + P(2,2) = 0.4 + 0.6 + 0.6 + 0 + 0.4 = 2