Final answer:
The chance that both books randomly chosen from the bookcase are statistics books is 3/28, which is found by multiplying the probabilities of each selection without replacement.
Step-by-step explanation:
To find the chance that both books chosen at random are statistics books, we need to calculate the probability of selecting one statistics book and then another one without replacement. Initially, there are 3 statistics books out of 8 total books. After one is chosen, there are 2 statistics books left out of 7 total books. The probability of choosing a statistics book first is 3/8, then the probability of choosing another statistics book is 2/7. Multiplying these two probabilities gives us the overall probability of both events happening consecutively:
(3/8) × (2/7) = 6/56 = 3/28.
Therefore, the chance that both books chosen are statistics books is 3/28, which corresponds to option c.