A fires 5 shots in the time B fires 3 shots. A hits (kills) once in 3 shots; B hits once in 2 shots. When B has missed 27 times, how many has A killed?

Given data

• Rate of fire: A : B = 5 : 3 (same time interval).
• Accuracy per shot: A hits with probability 1/3; B hits with probability 1/2 (miss prob = 1/2).
• B has missed 27 times.

Concept / Approach

• From B's miss probability (1/2), infer total shots fired by B; then scale to A's shots using the rate 5:3; finally compute A's kills using his hit probability (1/3).

Step-by-step calculationB's miss prob = 1/2 ⇒ expected misses = (1/2) × (B shots)27 = (1/2) × (B shots) ⇒ B shots = 54By firing-rate ratio, A shots = 54 × (5/3) = 90A's kills = (1/3) × 90 = 30

VerificationB's expected hits = (1/2) × 54 = 27; misses = 27 (as given). A's kills align with his accuracy.

Common pitfalls

• Using 5:3 as accuracy instead of rate of fire.
• Confusing B's misses with B's shots.

Final Answer30