|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
08 May 2020, 09:52
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
53% (02:36) correct
47%
(02:48)
wrong
based on 173
sessions
History
Date
Time
Result
Not Attempted Yet
A and B take part in a duel. A can strike with an accuracy of 0.6. B can strike with an accuracy of 0.8. A has the first shot, post which they strike alternately. What is the probability that A wins the duel?
A. 11/17
B. 15/23
C. 2/3
D. 7/10
E. 7/9
Are You Up For the Challenge: 700 Level Questions
A. 11/17
B. 15/23
C. 2/3
D. 7/10
E. 7/9
Are You Up For the Challenge: 700 Level Questions
08 May 2020, 22:16
Kudos
Bookmarks
Probability that A wins the duel on his first turn \(= 0.6\)
Probability that A wins the duel on his second turn \(= 0.4 * 0.2 *0.6\) (A and B miss on their first turn)
Probability that A wins the duel on his third turn \(= 0.4 * 0.2 *0.4 * 0.2*0.6= (0.4 * 0.2)^2 * 0.6\) (A and B miss on their first and second turn)
and so on
Probability that A wins the duel on his nth turn = \((0.4 * 0.2)^{n-1} * 0.6 \)
the probability that A wins the duel \(= 0.6 + (0.4 * 0.2) * 0.6+ (0.4 * 0.2)^2 * 0.6+.......\)upto infinite turns
Sum of infinite GP \(= \frac{a}{1-r} \){a=first term; r=common ratio}
the probability that A wins the duel \(= \frac{0.6}{[1-0.4*0.2] }= \frac{60}{92} = \frac{15}{23}\)
Probability that A wins the duel on his second turn \(= 0.4 * 0.2 *0.6\) (A and B miss on their first turn)
Probability that A wins the duel on his third turn \(= 0.4 * 0.2 *0.4 * 0.2*0.6= (0.4 * 0.2)^2 * 0.6\) (A and B miss on their first and second turn)
and so on
Probability that A wins the duel on his nth turn = \((0.4 * 0.2)^{n-1} * 0.6 \)
the probability that A wins the duel \(= 0.6 + (0.4 * 0.2) * 0.6+ (0.4 * 0.2)^2 * 0.6+.......\)upto infinite turns
Sum of infinite GP \(= \frac{a}{1-r} \){a=first term; r=common ratio}
the probability that A wins the duel \(= \frac{0.6}{[1-0.4*0.2] }= \frac{60}{92} = \frac{15}{23}\)
Bunuel
General Discussion
08 May 2020, 23:31
Kudos
Bookmarks
Bunuel
Probability of A striking = 0.6
i.e. Probability of A failing to strike = 1-0.6 = 0.4
Probability of B striking = 0.8
i.e. Probability of B failing to strike = 1-0.8 = 0.2
Case 1: A wins in first shot
Probability = 0.6
Case 2: A wins in second shot i.,e. sequence of strike is A Fail, B fails, A strikes
Probability \(= 0.4*0.2*0.6\)
Case 3: A wins in third shot i.,e. sequence of strike is A Fail, B fails, A Fail, B fails, A strikes
Probability \(= 0.4*0.2*0.4*0.2*0.6\)
and so on
Final Probability = Sum of all cases \(= 0.6*[1+(0.4*0.2)+(0.4*0.2)^2+...] = 0.6*[1+(0.08)+(0.08)^2+...] \)
CONCEPT: Sum of terms of an Infinite GP with common ratio r such that \(-1 < r < 1 = \frac{a}{(1-r)}\)
Final Probability \(= 0.6*[1+(0.08)+(0.08)^2+...] = 0.6*(\frac{1}{(1-0.08) }= 0.6*(\frac{1}{0.92}) = 60/92 = 15/23\)
