Using the below table:  A1A2B10.40.3B20.20.1 Compute P(A1 or B1).Compute P(A1 or B2).Calculate the marginal probabilities from the following table of joint probabilities.Determine P(A1 | B1).Determine P(A2 | B1).Did your answers to parts (a) and (b) sum to 1? Is this a coincidence? Explain.Calculate P(A1 | B2).Calculate P(A2 | B1).Are the events independent? Explain

Question
Asked Oct 11, 2019
  1. Using the below table:

 

 

A1

A2

B1

0.4

0.3

B2

0.2

0.1

 

  1. Compute P(A1 or B1).
  2. Compute P(A1 or B2).
  3. Calculate the marginal probabilities from the following table of joint probabilities.
  4. Determine P(A1 | B1).
  5. Determine P(A2 | B1).
  6. Did your answers to parts (a) and (b) sum to 1? Is this a coincidence? Explain.
  7. Calculate P(A1 | B2).
  8. Calculate P(A2 | B1).

Are the events independent? Explain

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Expert Answer

Step 1

Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If you want remaining sub-parts to be solved, then please resubmit the whole question and specify those sub-parts you want us to solve.

From the provided table the probabilities can be written as:

P(A) 0.6
P(A)0.4
P(B) 0.7
P(B,) 0.3
P(A and B) 0.4
P(A and B,) 0.2
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P(A) 0.6 P(A)0.4 P(B) 0.7 P(B,) 0.3 P(A and B) 0.4 P(A and B,) 0.2

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Step 2

1) The required probability of P(A1 or B1) can be calculated as:

P(4 or B) P(A)P(B,) - P(4 and B)
=0.6+0.7-0.4
0.9
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P(4 or B) P(A)P(B,) - P(4 and B) =0.6+0.7-0.4 0.9

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Step 3

2)  The required probability of P(A1 or B2) can ...

P(4 or B) P(4)+ P(B,)- P(4 and B,)
=0.6+0.3-0.2
0.7
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P(4 or B) P(4)+ P(B,)- P(4 and B,) =0.6+0.3-0.2 0.7

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