Events & Promotions
|
|
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.
Nov 2007:30 AM PST
-08:30 AM PST
Learn what truly sets the UC Riverside MBA apart and how it helps in your professional growth
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
30 Oct 2024, 10:16
Kudos
Bookmarks
Least probability: 0.70
Greatest probability: 0.80
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
27% (01:54) correct
73%
(02:23)
wrong
based on 541
sessions
History
Date
Time
Result
Not Attempted Yet
According to sports analysts, the New York Yankees have an 80% chance of winning the World Series in baseball, whereas the NY Jets have a 90% chance of winning the Superbowl.
Select for Least probability the least probability, compatible with the probabilities provided by the respective sports analysts, that both the New York Yankees and the NY Jets will win the World Series and Superbowl titles, and select for Greatest probability the greatest probability, jointly consistent with the probabilities provided by the respective sports analysts, that both the New York Yankees and the NY Jets will win the World Series and Superbowl titles. Make only two selections, one in each column.
Select for Least probability the least probability, compatible with the probabilities provided by the respective sports analysts, that both the New York Yankees and the NY Jets will win the World Series and Superbowl titles, and select for Greatest probability the greatest probability, jointly consistent with the probabilities provided by the respective sports analysts, that both the New York Yankees and the NY Jets will win the World Series and Superbowl titles. Make only two selections, one in each column.
| Least probability | Greatest probability | |
| 0.02 | ||
| 0.10 | ||
| 0.70 | ||
| 0.72 | ||
| 0.80 | ||
| 0.90 |
ShowHide Answer
Official Answer
Least probability: 0.70
Greatest probability: 0.80
31 Oct 2024, 12:00
Kudos
Bookmarks
1. We are given the probabilities of 2 events and are the asked to find the least and greatest probabilities of them both happening.
2. This is quite confusing to think about, so let’s try to draw it out. Probability can be thought of as sets. Let there be a box and point is randomly chosen.
3. The probability that the New York Yankees will win is 80% or 80% of the area in the box. The same goes for the probability that the NY Jets will win (90%).
4. Both of these probabilities are somehow merged together. Our question can be rephrased into finding the maximum and minimum probability of picking a point in both the green and blue areas.
5. The minimum probability happens when the two areas are as separated as possible.
In this case, it’s 70% or 0.70.
6. The maximum probability happens when the two areas are as merged as possible.
In this case, it’s 80% or 0.80.
7. Our answer will be: Least probability = 0.70 and Greatest probability = 0.80.
SportsArea1.jpg [ 26.68 KiB | Viewed 4610 times ]
SportArea2.jpg [ 39.38 KiB | Viewed 4568 times ]
SportsArea3.jpg [ 34.04 KiB | Viewed 4534 times ]
2. This is quite confusing to think about, so let’s try to draw it out. Probability can be thought of as sets. Let there be a box and point is randomly chosen.
3. The probability that the New York Yankees will win is 80% or 80% of the area in the box. The same goes for the probability that the NY Jets will win (90%).
4. Both of these probabilities are somehow merged together. Our question can be rephrased into finding the maximum and minimum probability of picking a point in both the green and blue areas.
5. The minimum probability happens when the two areas are as separated as possible.
In this case, it’s 70% or 0.70.
6. The maximum probability happens when the two areas are as merged as possible.
In this case, it’s 80% or 0.80.
7. Our answer will be: Least probability = 0.70 and Greatest probability = 0.80.
Attachment:
SportsArea1.jpg [ 26.68 KiB | Viewed 4610 times ]
Attachment:
SportArea2.jpg [ 39.38 KiB | Viewed 4568 times ]
Attachment:
SportsArea3.jpg [ 34.04 KiB | Viewed 4534 times ]
26 Nov 2024, 20:19
Kudos
Bookmarks
This is a hidden overlapping sets question, so I'll use the 2-dimension matrix to illustrate:
Because a team either wins or loses, so the total probability is 1. Therefore, the probability that Yankees loses is 1 - 0.8 = 0.2, Jet loses is 1 - 0.9 = 0.1
The question asks to find the least and the greatest probability that both Yankees and Jets win, which means to find min and max value of x
- To find min(x), we need to find max(a). Max(a) = 0.2 (in this case, b = 0). So min(x) will be 0.9 - 0.2 = 0.7
- To find max(x), let's try a = 0 or c = 0
Therefore, the least probability that both Yankees and Jets win is 0.7 and the greatest probability is 0.8
| Yankees wins | Yankees loses | Total probability | |
| Jets wins | x | a | 0.9 |
| Jets loses | c | b | 0.1 |
| Total probability | 0.8 | 0.2 | 1 |
Because a team either wins or loses, so the total probability is 1. Therefore, the probability that Yankees loses is 1 - 0.8 = 0.2, Jet loses is 1 - 0.9 = 0.1
The question asks to find the least and the greatest probability that both Yankees and Jets win, which means to find min and max value of x
- To find min(x), we need to find max(a). Max(a) = 0.2 (in this case, b = 0). So min(x) will be 0.9 - 0.2 = 0.7
- To find max(x), let's try a = 0 or c = 0
- If a = 0 then b = 0.2, which higher than the total probability of Jet loses (0.1) => eliminate
- If c = 0 then b = 0.1, a = 0.1, x = 0.8 => compatible with the probabilities provided
Therefore, the least probability that both Yankees and Jets win is 0.7 and the greatest probability is 0.8
