An Anti Aircraft Gun can Fire Four Shots at a Time GMAT Problem Solving

Question: An anti aircraft gun can fire four shots at a time. If the probabilities of the first, second, third and the last shot hitting the enemy aircraft are 0.7, 0.6, 0.5 and 0.4, what is the probability that four shots aimed at an enemy aircraft will bring the aircraft down?

(A) 0.084
(B) 0.916
(C) 0.036
(D) 0.964
(E) 0.92

Correct Answer: D
Solution and Explanation:
Approach Solution 1:
So, we want P(at least one shot hits the aircraft)
When it comes to probability questions involving "at least," it's best to try using the complement.
That is, P(Event A happening) = 1 - P(Event A not happening)
So, here we get: P(at least 1 shot hits plane) = 1 - P(zero shots hit plane)
P(zero shots hit plane)
P(zero shots hit plane) = P(1st shot misses AND 2nd shot misses AND 3rd shot misses AND 4th shot misses)
= P(1st shot misses) x P(2nd shot misses) x P(3rd shot misses) x P(4th shot misses)
= 0.3 x 0.4 x 0.5 x 0.6
= 3/10 x 4/10 x 5/10 x 6/10
= 360/10000
= 0.036
So....…
P(at least 1 shot hits plane) = 1 - P(zero shots hit plane)
= 1 - 0.036
= 0.964

Approach Solution 2:
Probabilities of the first, second, third and the last shot hitting the enemy aircraft are 0.7, 0.6, 0.5 and 0.4
Sum of probabilities of each shot= 0.7+0.3*0.6+0.3*0.4*0.5+0.3*0.4*0.5*0.4
=0.964

Approach Solution 3:
The enemy aircraft will be brought down even if one of the four shots hit the aircraft.
The opposite of this situation is that none of the four shots hit the aircraft.
The probability that none of the four shots hit the aircraft is given by:
(1-0.7)(1-0.6)(1-0.5)(1-0.4) = 0.3×0.4×0.5×0.6 = 0.036
So, the probability that at least one of the four shots hit the aircraft:
=1-0.036 = 0.964

“An anti aircraft gun can fire four shots at a time. If the probabilities”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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