Answer:

There are a total of eight books on the shelf, three of which are geometry books and five of which are algebra books. If two books are taken without replacement, there are a total of 8 x 7 = 56 possible ways that the two books can be chosen.

To calculate the probability that the first book chosen is a geometry book and the second book chosen is an algebra book, we can use the following formula:

P(G then A) = P(G) * P(A | G)

where P(G) is the probability of choosing a geometry book first, and P(A | G) is the probability of choosing an algebra book second given that the first book chosen was a geometry book.

The probability of choosing a geometry book first is 3/8, since there are three geometry books out of a total of eight books.

Once a geometry book has been chosen, there are seven books remaining, including four algebra books. Therefore, the probability of choosing an algebra book second given that the first book chosen was a geometry book is 4/7.

Therefore, the probability of choosing a geometry book first and an algebra book second is:

P(G then A) = P(G) * P(A | G)

P(G then A) = (3/8) * (4/7)

P(G then A) = 12/56

P(G then A) = 3/14

Therefore, the probability that the first book is geometry and the second book is algebra is 3/14, or approximately 0.214.