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705-805 Level|   Graphs|   Math Related|      
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A certain product must be subjected to (and pass) a sequence of variou 30 Apr 2024, 10:27
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Dropdown 1: 0.02 Dropdown 2: 0.91
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75% (hard)

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71% (03:13) correct 29% (03:25) wrong based on 1033 sessions

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A certain product must be subjected to (and pass) a sequence of various combinations of 5 tests (Tests A through E) before it may receive one of two certifications (Certification 1 or Certification 2). The diagram shows how products proceed through these tests, along with the probability of proceeding from each test to the next test or certification. For instance, the diagram shows that an item subjected to Test A has a 0.20 probability of passing Test A and being subjected to Test B next, a 0.75 probability of passing Test A and being subjected to Test C next, and a 0.05 probability of failing Test A. The probability that an item receives either of the two certifications is exactly 0.93.

Based on the information provided, select from each drop-down menu the option that creates the most accurate statement.

To the nearest hundredth, the probability that a randomly selected product subjected to Test A will receive Certification 1 is .

To the nearest hundredth, the probability that a randomly selected product subjected to Test A will receive Certification 2 is .
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Dropdown 1: 0.02 Dropdown 2: 0.91
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Ami0Trafalgar
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A certain product must be subjected to (and pass) a sequence of variou 03 May 2024, 00:44
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Ridss

A certain product must be subjected to (and pass) a sequence of various combinations of 5 tests (Tests A through E) before it may receive one of two certifications (Certification 1 or Certification 2). The diagram shows how products proceed through these tests, along with the probability of proceeding from each test to the next test or certification. For instance, the diagram shows that an item subjected to Test A has a 0.20 probability of passing Test A and being subjected to Test B next, a 0.75 probability of passing Test A and being subjected to Test C next, and a 0.05 probability of failing Test A. The probability that an item receives either of the two certifications is exactly 0.93.

Based on the information provided, select from each drop-down menu the option that creates the most accurate statement.

To the nearest hundredth, the probability that a randomly selected product subjected to Test A will receive Certification 1 is [dropdown1]

To the nearest hundredth, the probability that a randomly selected product subjected to Test A will receive Certification 2 is  [dropdown2]
options : 0.86 , 0.91



­
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Correct Answer:
Dropdown 1: 0.02
Dropdown 2: 0.91
­
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­For Question 1,
Probability of Test A receiving Certificate 1 will only have 1 path:
A --> B --> D --> Certificate 1
= 0.2 * 0.2 * 0.5 = 0.020

­For Question 2,
Probability of Test A receiving Certificate 2 will only have 4 paths:
A --> C --> E --> Certificate 2 = 0.75 * 0.25 * 1.00 = [3][/16]
A --> C --> Certificate 2 = 0.75 * 0.75 = [9][/16]
A --> B --> E --> Certificate 2 = 0.2 * 0.7 * 1.00 = [7][/50]
A --> B --> D --> Certificate 2 = 0.2 * 0.2 * 0.5 = [1][/50]

Adding the probability of all possible paths, 
[3][/16] + [9][/16] + [7][/50] + [1][/50] = [12][/16] + [8][/50] = [91][/100] = 0.91
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rotesque
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A certain product must be subjected to (and pass) a sequence of variou 02 May 2024, 18:49
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To the nearest hundredth, the probability that a randomly selected product subjected to Test A will receive Certification 1 is [0.20 * 0.40 * 0.93 = 0.074]"

For the second statement:

"To the nearest hundredth, the probability that a randomly selected product subjected to Test A will receive Certification 2 is [0.20 * 0.60 * 0.93 = 0.111]"

These calculations account for the probabilities provided for each step in the process.
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A certain product must be subjected to (and pass) a sequence of variou 28 Jun 2024, 07:12
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Ridss

A certain product must be subjected to (and pass) a sequence of various combinations of 5 tests (Tests A through E) before it may receive one of two certifications (Certification 1 or Certification 2). The diagram shows how products proceed through these tests, along with the probability of proceeding from each test to the next test or certification. For instance, the diagram shows that an item subjected to Test A has a 0.20 probability of passing Test A and being subjected to Test B next, a 0.75 probability of passing Test A and being subjected to Test C next, and a 0.05 probability of failing Test A. The probability that an item receives either of the two certifications is exactly 0.93.

Based on the information provided, select from each drop-down menu the option that creates the most accurate statement.

To the nearest hundredth, the probability that a randomly selected product subjected to Test A will receive Certification 1 is [dropdown1]

To the nearest hundredth, the probability that a randomly selected product subjected to Test A will receive Certification 2 is  [dropdown2]
options : 0.86 , 0.91



­
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Correct Answer:
Dropdown 1: 0.02
Dropdown 2: 0.91
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­I am sure the value 0.93 in the question is given for a reason. If you add P(1) and P(2), the answer should be 0.93.
Thus, the values in first dropdown and second dropdown should add to 0.93...Pretty straightforward.

However, even if you calculate values for individual certificate, you will get the answer. But they wouldn't give probability of either be 0.93 in that case.

Solution in case we didn't know the dropdowns as in here.

Certificate 2 can be received through three routes, and tests C and E move towards only 2 and have probability of passing as 1.
a) The moment test C is given, it is 100% to result in certificate 2 ( as C and E have a 100% probability of pbeing passed)
Probabilty of moving from A to C is 0.75
b) Next, if we move from A to B, the probability is 0.2, and moving to C is 0.70. Thus probabilty of reaching C via B is 0.2*0.70 or 0.14
We know beyond C, probabilty is 100%.
C) Finally, if we move from A to B , the probability is 0.2, then B to D is again 0.2 and moving to E is 0.50. Thus probabilty of reaching E via B and D is 0.2*0.2*0.5 or 0.02
We know beyond E, probabilty is 100%.
Total P = 0.75+0.14+0.02 = 0.91

In the actuals, you will not have to solve this long, and two ways to answer
(1) Add the two dropdowns to get 0.93
(2) Find P of 1, which is 0.2*0.2*0.5 or 0.02, and for dropdown 2, just subtract this from 0.93 or 0.93-0.02, that is 0.91

SATYAM7777
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A certain product must be subjected to (and pass) a sequence of variou 15 Aug 2024, 02:20
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I’ve been following this thread and want to add my thoughts based on the discussion. To summarize:

For Certification 1:
The only path that leads to Certification 1 from Test A involves:
  • A → B → D → Certification 1
The probability for this path is:

0.20(A to B)×0.20(B to D)×0.50(D to Certification 1)=0.02

So, the probability of receiving Certification 1 from Test A is 0.02 (or 2%).

For Certification 2:
There are several paths leading to Certification 2:

Path A → C → E → Certification 2:
0.75(A to C)×0.25(C to E)×1.00(E to Certification 2)=0.1875
Path A → C → Certification 2:
0.75(A to C)×0.75(C to Certification 2)=0.5625
Path A → B → E → Certification 2:
0.20(A to B)×0.70(B to E)×1.00(E to Certification 2)=0.14
Path A → B → D → Certification 2:
0.20(A to B)×0.20(B to D)×0.50(D to Certification 2)=0.02
Adding these probabilities gives us:
0.1875+0.5625+0.14+0.02=0.91

Thus, to satisfy the condition that the total probability for receiving either of the certifications is 0.93, the probabilities are:
  • Certification 1: 0.02
  • Certification 2: 0.91
This fits with the total probability of 0.93 as required. So the correct probabilities to fill in are:
  • Certification 1: 0.02
  • Certification 2: 0.91
Hope this helps clear things up!­
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A certain product must be subjected to (and pass) a sequence of variou 30 Dec 2024, 04:45
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Ridss


A certain product must be subjected to (and pass) a sequence of various combinations of 5 tests (Tests A through E) before it may receive one of two certifications (Certification 1 or Certification 2). The diagram shows how products proceed through these tests, along with the probability of proceeding from each test to the next test or certification. For instance, the diagram shows that an item subjected to Test A has a 0.20 probability of passing Test A and being subjected to Test B next, a 0.75 probability of passing Test A and being subjected to Test C next, and a 0.05 probability of failing Test A. The probability that an item receives either of the two certifications is exactly 0.93.

Based on the information provided, select from each drop-down menu the option that creates the most accurate statement.

To the nearest hundredth, the probability that a randomly selected product subjected to Test A will receive Certification 1 is .

To the nearest hundredth, the probability that a randomly selected product subjected to Test A will receive Certification 2 is .


­
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Correct Answer:
Dropdown 1: 0.02
Dropdown 2: 0.91
­
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There is only 1 way of reaching Certification 1 from A: A->B->D->Certification 1
0.2 * 0.2 * 0.5 = .02

There are many ways of reaching Certification 2 and we cannot be expected to calculate all those in the limited time.
They have given us that "The probability that an item receives either of the two certifications is exactly 0.93" We also know that the item will receive only one of two certifications (not both)

Hence 0.93 = .02 + P(Certificate 2)
P(Certificate 2) = 0.91

Select 0.02 and 0.91
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A certain product must be subjected to (and pass) a sequence of variou 06 Mar 2025, 01:43
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Wow, the breakdown of probabilities is super helpful! I love how it shows the paths to certifications. Makes it clearer how they arrived at that 0.93 figure. Can't wait to dive deeper into this!
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A certain product must be subjected to (and pass) a sequence of variou 06 Mar 2025, 06:06
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for getting certification 1(C1) probability =0.2*0.2*0.5= 0.02
and if we look at last sentence of sthe statement we will see probability of reciving either of the certificate is 0.93, which means probability of getting certification 2(C2)
=0.93-0.02
=0.91 (here its clearly stated in statement that they will get only one certification)
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