Question

What gives the greater probability of hitting some target at least once: hitting in a shot with probability ¼ and firing 2 shots or hitting in a shot with probability ½ and firing 1 shot? Explain how you arrived at your answer. What gives the greater probability of hitting some target at least once: hitting in a shot with probability ¼ and firing 2 shots or hitting in a shot with probability ½ and firing 1 shot? Explain how you arrived at your answer. @Mathematics

Answer 1

The probability of hitting the target at least once in 2 shots is 1 minus the probability of missing the target after firing 2 shots.\[1-\left(\frac{3}{4}\right)^2=\frac{7}{16} \]Better to take one shot with a probability of 1/2.\[\frac{7}{16}<\frac{8}{16} \]