Explanation
1. Define the Probabilities of Hitting
Let P(H1),P(H2),P(H3), and P(H4) be the probabilities of hitting the plane on the 1st, 2nd, 3rd, and 4th shots respectively.
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P(H1)=0.4
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P(H2)=0.3
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P(H3)=0.2
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P(H4)=0.1
2. Find the Probabilities of Missing
The probability of missing a shot is 1−P(Hit).
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P(Miss1)=1−0.4=0.6
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P(Miss2)=1−0.3=0.7
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P(Miss3)=1−0.2=0.8
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P(Miss4)=1−0.1=0.9
3. Calculate the Probability of Missing All Shots
The gun fails to hit the plane only if it misses all four shots. Since the shots are independent:
P(Miss all)=P(Miss1)×P(Miss2)×P(Miss3)×P(Miss4)
P(Miss all)=0.6×0.7×0.8×0.9
4. Calculate the Probability of Hitting the Plane
The probability of hitting the plane is the complement of missing all shots:
Correct Option: (c) 0.6976
