Source: Economist GMAT
A game at the state fair has a circular target with a radius of 10 cm on a square board measuring 30 cm on a side. Players win prizes if they throw two darts and hit only the circular area on both throws. If Jim hit the board on both throws, what is the probability that Jim won the game?
A. 1/3
B. 1/9
C. π/9
D. π^2/81
E. π^2/9
The OA is D.
A game at the state fair has a circular target with a radius
This topic has expert replies
-
- Moderator
- Posts: 2209
- Joined: Sun Oct 15, 2017 1:50 pm
- Followed by:6 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
$$? = P\left( {2\,\,{\rm{hits}}\,\,{\rm{in}}\,\,{\rm{circular}}\,\,{\rm{region}}\,\,{\rm{in}}\,\,{\rm{two}}\,\,{\rm{throws}}} \right)$$BTGmoderatorLU wrote:Source: Economist GMAT
A game at the state fair has a circular target with a radius of 10 cm on a square board measuring 30 cm on a side. Players win prizes if they throw two darts and hit only the circular area on both throws. If Jim hit the board in random points on both throws, what is the probability that Jim won the game?
A. 1/3
B. 1/9
C. π/9
D. π^2/81
E. π^2/9
We may consider the similar figure(!) in which the radius of the circular target is 1cm and the square board has 3cm on a side.
$$P\left( {1\,\,{\rm{hit}}\,\,{\rm{in}}\,\,{\rm{circular}}\,\,{\rm{region}}\,\,{\rm{in}}\,\,{\rm{one}}\,\,{\rm{throw}}} \right) = {{{S_{{\rm{circle}}}}} \over {{S_{{\rm{square}}}}}} = {{\pi \cdot {1^2}} \over {{3^2}}} = {\pi \over 9}$$
$$? = {\left( {{\pi \over 9}} \right)^2}\,\,\,{\rm{by}}\,\,{\rm{independency}}\,\,{\rm{on}}\,\,{\rm{throws}}$$
The correct answer is therefore (D).
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Area of the circle = πr^2 = π*10^2 = 100π cm^2BTGmoderatorLU wrote:Source: Economist GMAT
A game at the state fair has a circular target with a radius of 10 cm on a square board measuring 30 cm on a side. Players win prizes if they throw two darts and hit only the circular area on both throws. If Jim hit the board on both throws, what is the probability that Jim won the game?
A. 1/3
B. 1/9
C. π/9
D. π^2/81
E. π^2/9
The OA is D.
Area of the square = 30*30 = 900 cm^2
Probability of hitting ONE dart within the circle = (Area of the circle) / (Area of the square) = 100π / 900 = π/9
Probability of hitting both the darts within the circle = π/9* π/9 = π^2/81
The correct answer: D
Hope this helps!
-Jay
_________________
Manhattan Review GMAT Prep
Locations: Manhattan Review India | Mehdipatnam GMAT Coaching | Madhapur GMAT Courses | Manhattan Review Hyderabad | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7247
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
TBTGmoderatorLU wrote:Source: Economist GMAT
A game at the state fair has a circular target with a radius of 10 cm on a square board measuring 30 cm on a side. Players win prizes if they throw two darts and hit only the circular area on both throws. If Jim hit the board on both throws, what is the probability that Jim won the game?
A. 1/3
B. 1/9
C. π/9
D. π^2/81
E. π^2/9
he area of the circular target of the board is 100� cm^2 and the area of the entire board is 900 cm^2, so the probability of hitting the target once is 100�/900, or �/9. The probability of hitting the target twice is:
�/9 x �/9 = �^2/81
Answer: D
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews