Three cannons are firing at a target.

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

NandishSS: Master | Next Rank: 500 Posts; Posts: 366; Joined: Fri Jun 05, 2015 3:35 am; Thanked: 3 times; Followed by:2 members

Three cannons are firing at a target.

by NandishSS » Sun Apr 22, 2018 6:32 am

Three cannons are firing at a target. If their individual probabilities to hit the target are 0.3, 0.4, and 0.5 respectively, what is the probability that none of the cannons will hit the target after one round of fire?

A. 0.06
B. 0.12
C. 0.21
D. 0.29
E. 0.94

[spoiler]OA: C[/spoiler]

HI Experts

Why is below ans incorrect?

P [None] = 1 - P [all hit target]
= 1 - (0.3) (0.4) (0.5)
= 0.94

Thanks
Nandish

Quote

Source: Beat The GMAT — Problem Solving | Sun Apr 22, 2018 6:32 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sun Apr 22, 2018 6:37 am

NandishSS wrote:Three cannons are firing at a target. If their individual probabilities to hit the target are 0.3, 0.4, and 0.5 respectively, what is the probability that none of the cannons will hit the target after one round of fire?

A. 0.06
B. 0.12
C. 0.21
D. 0.29
E. 0.94

P(1st MISSES target) = 1 - P(1st HITS target) = 1 - 0.3 = 0.7
P(2nd MISSES target) = 1 - P(2nd HITS target) = 1 - 0.4 = 0.6
P(3rd MISSES target) = 1 - P(3rd HITS target) = 1 - 0.5 = 0.5
----------------------------

P(none hit the target) = P(1st misses target AND 2nd misses target AND 3rd misses target)
= P(1st misses target) x P(2nd misses target) x P(3rd misses target)
= 0.7 x 0.6 x 0.5
= 0.21

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Quote

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sun Apr 22, 2018 6:42 am

NandishSS wrote:Three cannons are firing at a target. If their individual probabilities to hit the target are 0.3, 0.4, and 0.5 respectively, what is the probability that none of the cannons will hit the target after one round of fire?

A. 0.06
B. 0.12
C. 0.21
D. 0.29
E. 0.94

[spoiler]OA: C[/spoiler]

HI Experts

Why is below ans incorrect?

P [None] = 1 - P [all hit target]
= 1 - (0.3) (0.4) (0.5)
= 0.94

Thanks
Nandish

P[all shots hit target] is not the complement of P[no shots hit target]

If what is the opposite of "none of the shots hit the target"?
Well, it's can be 1 shot hits target or 2 shots hit target or all 3 shots hit target.
So, if we're going to use the complement here, we must consider all 3 cases.

That is:
P(no shots hit target) = 1 - P(1 shot hits target OR 2 shots hit target OR all 3 shots hit target)
Lots of work!!!

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Apr 24, 2018 10:48 am

NandishSS wrote:Three cannons are firing at a target. If their individual probabilities to hit the target are 0.3, 0.4, and 0.5 respectively, what is the probability that none of the cannons will hit the target after one round of fire?

A. 0.06
B. 0.12
C. 0.21
D. 0.29
E. 0.94

We need to calculate the probability that none of the 3 cannons will hit the target. P(cannons not hitting) = 0.7 x 0.6 x 0.5 = 0.21.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]