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Previous Year Question (PYQs)



An anti-aircraft gun fires a maximum of four shots. Probabilities of hitting in the 1st, 2nd, 3rd, and 4th shot are 0.4, 0.3, 0.2 and 0.1 respectively. Find the probability that the gun hits the plane.





Solution

Hit at least once = 1 − (miss all shots) 
Miss probabilities: 
1st: $(1 - 0.4) = 0.6$ 
2nd: $(1 - 0.3) = 0.7$ 
3rd: $(1 - 0.2) = 0.8$ 
4th: $(1 - 0.1) = 0.9$ 
Miss all: $0.6 \cdot 0.7 \cdot 0.8 \cdot 0.9 = 0.3024$ 
Hit at least once: $1 - 0.3024 = 0.6976$


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