1. **State the problem:** Calculate the value of the expression $\frac{50}{3} + 32 - 2$.\n\n2. **Recall the order of operations:** Division and multiplication are performed before addition and subtraction.\n\n3. **Perform the division first:** $\frac{50}{3} = 16.\overline{6}$ (approximately 16.6667).\n\n4. **Substitute back and simplify:** $16.\overline{6} + 32 - 2$.\n\n5. **Add and subtract in order:** $16.\overline{6} + 32 = 48.\overline{6}$, then $48.\overline{6} - 2 = 46.\overline{6}$.\n\n6. **Final answer:** The value of the expression is approximately $46.67$.