1. **State the problem:** Jim has 9 pieces of fruit: 7 grapefruits and 2 apples. He picks one fruit at random and eats it, then picks a second fruit at random. We want to find the probabilities labeled A and B on the probability tree for the second pick after the first pick was an apple. 2. **Understand the tree:** - First pick: 7/9 chance grapefruit, 2/9 chance apple. - If first pick grapefruit: second pick probabilities are 6/8 grapefruit and 2/8 apple (since one grapefruit is eaten, 6 grapefruits left out of 8 total fruits left). - If first pick apple: second pick probabilities are unknown (A for grapefruit, B for apple). 3. **Calculate A and B:** - After eating one apple, remaining fruits: 7 grapefruits and 1 apple (total 8 fruits). - Probability second pick is grapefruit (A) = number of grapefruits left / total fruits left = $\frac{7}{8}$. - Probability second pick is apple (B) = number of apples left / total fruits left = $\frac{1}{8}$. 4. **Summary:** - $A = \frac{7}{8}$ - $B = \frac{1}{8}$ These fractions are already in simplest form. **Final answer:** $$A=\frac{7}{8},\quad B=\frac{1}{8}$$