There are two lines of defense against an attacking aircraft, the firs

Question

There are two lines of defense against an attacking aircraft, the first is a missile and the second an anti-aircraft gun. The respective probabilities that the aircraft being hit by the missile and the gun are 2/9 and 1/8, respectively. What is the probability of hitting the aircraft ?

A. 23/72
B. 1/3
C. 25/72
D. 13/36
E. 3/8

A. 23/72
B. 1/3
C. 25/72
D. 13/36
E. 3/8

Mona2019 · Answer

Probability of hitting the aircraft = 1-probability of none hitting the aircraft
= 1-((7/9)*(7/8))
= 23/72

IMO A

Posted from my mobile device

GMATinsight · Answer

Probability of Gun not hitting the aircraft  = (1-\frac{1}{8}) = \frac{7}{8}

Probability of Missile not hitting the aircraft  = (1-\frac{2}{9}) = \frac{7}{9}

Probability that none of the missile and gun Hit the aircraft  = \frac{7}{8}*\frac{7}{9} = \frac{49}{72}

Probability of Hitting the aircraft  = 1- \frac{49}{72} = \frac{23}{72}

Answer: Option A

GMATwithAK · Answer

Let's look at this from the perspective of the surviving aircrafts.

7 out of 9 aircrafts will survive the missile.
7 out of 8 aircraft will survive the gun.

That is 49 out of 72 aircrafts will survive

Aircrafts which would survive = 7/9 * 7/8 = 49/72

Aircrafts which will not survive = 1 -   = 23 / 72

That's 23 aircrafts out of every 72 aircrafts which won't survive.

So, answer is option A

ScottTargetTestPrep · Answer

Solution:
 
We use the complement rule to solve this problem. There are 4 possible outcomes in this scenario, where H = the aircraft is hit and N = the aircraft is not hit:

(H, H) means the aircraft is hit by both the missile and the gun
(H, N) means the aircraft is hit by the missile but not the gun
(N, H) means the aircraft is not hit by the missile but is hit by the gun
(N, N) means the aircraft is hit by neither the missile nor the gun

Note that any of the first 3 outcomes would indicate a hit. So only the fourth outcome (N, N) is the outcome where the aircraft is not hit. Thus, it is easier to calculate the probability of (N, N) and subtract this probability from 1 (using the rule of the complement) to find the probability that the aircraft is hit.

The probability of not hitting the aircraft by either the missile or the gun - (N, N) - is (1 - 2/9) x (1 - 1/8) = 7/9 x 7/8 = 49/72. Thus, the probability of hitting the aircraft is 1 - 49/72 = 23/72.

Answer: A

Fdambro294 · Answer

The listing of the Completely Exhaustive events:

P(Missile Hits and Gun Misses)

+

P(Missile Misses and Gun Hits)

+

P(BOTH Missile and Gun Hit)

+

P(NEITHER Hit)

=

1

1 - P(Neither Hit) = Probability that the plane is Hit

Or, the long way

P(Missile Hits and Gun Misses) = (2/9) (7/8) = 14/72

+

P(Missile misses and Gun Hits) = (7/9) (1/8) = 7/72

+

P(Missile Hits and Gun Hits) = (2/9) (1/8) = 2/72

14/72 + 7/72 + 2/72 = 23/72

Posted from my mobile device

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

There are two lines of defense against an attacking aircraft, the firs

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

There are two lines of defense against an attacking aircraft, the firs

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards