Answer: Consider the endothermic reactions in Exercise

Chapter 2, Problem 132E

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QUESTION:

Consider the endothermic reactions in Exercise 2-50. Let 𝐴 denote the event that a reaction's inal temperature is 271 K or less. Let 𝐵 denote the event that the heat absorbed is above target. Determine the following probabilities.

(a) \(P(A \cap B)\)         (b) \(P(A \cup B)\)         (c) \(P\left(A^{\prime} \cup B^{\prime}\right)\)        (d) Use the total probability rule to determine P(A)

Equation transcription:

Text transcription:

P(A cap B)

P(A cup B)

P(A^{prime} cup B^{prime})

Questions & Answers

QUESTION:

Consider the endothermic reactions in Exercise 2-50. Let 𝐴 denote the event that a reaction's inal temperature is 271 K or less. Let 𝐵 denote the event that the heat absorbed is above target. Determine the following probabilities.

(a) \(P(A \cap B)\)         (b) \(P(A \cup B)\)         (c) \(P\left(A^{\prime} \cup B^{\prime}\right)\)        (d) Use the total probability rule to determine P(A)

Equation transcription:

Text transcription:

P(A cap B)

P(A cup B)

P(A^{prime} cup B^{prime})

ANSWER:

Solution:

Step 1 of 5:

The summarized data regarding 204 endothermic reactions is given

Final temperature conditions

                             Heat absorbed (cal)

Below target

Above target

266 K

12

40

271 K

44

16

274 K

56

36

Also, it is given that A denote the event the reaction’s final temperature is 271 K or less and B denotes the event that the heat absorbed is above target.

Using this, we need to find the required values.


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