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Consider three sets E1 = {1, 2, 3}, F1 = {1, 3, 4} and G1 = {2, 3, 4, 5}. Two elements are chosen at random, without replacement, from the set E1 and let S1 denote the set of these chosen elements. Let E2 = E1 - S1 and F2 = F1 ∪ S1. Now, two elements are chosen at random, without replacement, from the set F2 and let Sdenote the set of these chosen elements. Let G2 = G1 ∪ S2. Finally, two elements are chosen at random, without replacement, from the set G2 and let S3 denote the set of these chosen elements. Let E3 = E2 ∪ S3. Given that E1 = E3, let p be the conditional probability of the event S1 = {1, 2}. Then the value of p is
  • a)
    1/5
  • b)
    3/5
  • c)
    1/2
  • d)
    2/5
Correct answer is option 'A'. Can you explain this answer?
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Consider three sets E1= {1, 2, 3}, F1= {1, 3, 4} and G1= {2, 3, 4, 5}....
- S1and G2= G1- S1be the sets of remaining elements in E1, F1, and G1, respectively.

a) List all the elements in S1.

There are three possible ways to choose two elements from E1 without replacement: {1,2}, {1,3}, and {2,3}. Therefore, S1 could be {1,2}, {1,3}, or {2,3}.

b) List all the elements in E2, F2, and G2.

If S1= {1,2}, then E2= {3}, F2= {1,3,4}, and G2= {3,4,5}.

If S1= {1,3}, then E2= {2}, F2= {3,4}, and G2= {2,4,5}.

If S1= {2,3}, then E2= {1}, F2= {1,4}, and G2= {4,5}.
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Consider three sets E1= {1, 2, 3}, F1= {1, 3, 4} and G1= {2, 3, 4, 5}....


Conditional Probability = 
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Consider three sets E1= {1, 2, 3}, F1= {1, 3, 4} and G1= {2, 3, 4, 5}. Two elements are chosen at random, without replacement, from the set E1and let S1denote the set of these chosen elements. Let E2= E1- S1and F2= F1∪S1. Now, two elements are chosen at random, without replacement, from the set F2and let S2denote the set of these chosen elements.Let G2= G1∪S2. Finally, two elements are chosen at random, without replacement, from the set G2and let S3denote the set of these chosen elements.Let E3= E2∪S3. Given that E1= E3, let p be the conditional probability of the event S1= {1, 2}. Then the value of p isa)1/5b)3/5c)1/2d)2/5Correct answer is option 'A'. Can you explain this answer?
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