Sam can hit a target 1 time in 4 shots, Jack can hit the target 2 times in 4 shots and Raj can hit the target 6 times in 6 shots. What is the probability that at least 2 shots hit the target?
Solution
✅ Correct Option: 3
| Person | Given | Hits | Misses | |---|---|---|---| | Sam | 1 in 4 shots | $\dfrac{1}{4}$ | $\dfrac{3}{4}$ | | Jack | 2 in 4 shots | $\dfrac{2}{4}=\dfrac{1}{2}$ | $\dfrac{1}{2}$ | | Raj | 6 in 6 shots | $\dfrac{6}{6}=1$ | $0$ | Raj never misses, so one hit is already guaranteed. To get at least 2 hits we only need at least one hit from Sam or Jack. It is quicker to find the opposite case, where both of them miss. $P(\text{both miss})=\dfrac{3}{4}\times\dfrac{1}{2}=\dfrac{3}{8}$ $P(\text{at least 2 hits})=1-\dfrac{3}{8}=\dfrac{5}{8}$