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# Answer: Consider the endothermic reactions in Exercise

## Problem 132E Chapter 2.5

Applied Statistics and Probability for Engineers | 6th Edition

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Applied Statistics and Probability for Engineers | 6th Edition

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Problem 132E

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

Step-by-Step 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.

Step 2 of 5:

(a)

Here we have to find the value of P(AB).

AB denotes the event that the temperature of the reaction is 271 K or less and the heat of the reaction is above target.

The outcomes favouring this event are 40+16 and total number of outcomes is       12+44+56+40+16+36=204.

So the value of P(AB) becomes

P(AB)=

=

=0.2745

Thus, P(AB)=0.2745.

Step 3 of 5:

(b)

Here we have to find the value of P(AB).

AB denotes the event that the final temperature of the reaction is 271 K or less or the heat is above target.

The outcomes favouring this event are 12+44+40+16+36 and the total number of outcomes is 204.

So, the value of P(AB) become

P(AB)=

=

=0.7255

Thus, P(AB)=0.7255.

Step 4 of 5

Step 5 of 5

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