What is the probability of rolling an even number followed by another even number on a number cube labeled 1-6? a) 1/4; dependent b) 1/5; dependent c) 1/4; independent d) 1/5; independent

The sample space is 
S = {1,2,3,4,5,6}
which is the set of all possible outcomes

The event space is the list of things we want to happen, namely getting an even number
E = {2,4,6}

We have 3 items in the event space out of 6 items total
Therefore, the probability that we land on an even number is 3/6 = 1/2

Each roll is independent from any other roll. The dice is said to have "no memory" meaning that past events do not affect future rolls. So we can use the rule
P(A and B) = P(A)*P(B)
P(A and B) = (1/2)*(1/2)
P(A and B) = 1/4
where A and B represent rolling an even number for the first and second tries



In summary, the answer is 1/4; independent which is choice C

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