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Consider the endothermic reactions in the table below.

Final Temperature Conditions Heat Absorbed (cal)
Below Target Above Target
266 K 13 40
271 K 44 17
274 K 56 36
Let denote the event that a reaction's final temperature is 271 K or less. Let denote the event that the heat absorbed is above target. Determine the following probabilities.
A) P(AUB).
B) P(A'UB').
C) Use the total probability rule to determine P(A).

User Davidselo
by
6.4k points

1 Answer

4 votes

Answer:

0.277

0.723

0.553

Explanation:

Given the data:

Final temp condtn__ below target __above

266K ____________ 13 __________ 40

271 K ____________ 44 __________ 17

274 K ____________ 56 _________ 36

A = final temp ≤ 271K : {44, 40, 13, 17}

Total = {13 + 40 + 44 + 17 + 56 + 36}= 206

B = heat absorbed is above target : {40, 17, 36}

P(AuB) :

AuB = {40, 17} = (40 + 17) = 57

P(AuB} = (AuB) / total = 57 /206 = 0.277

A' = {36, 56,}

B' = {13, 44, 56}

(A'uB') = {36 + 56 + 13 + 44} = 149

P(A'uB') = 149 / 206 = 0.723

P(A) = (44 + 40 + 13 + 17) / 206 = 0.553

User Rahulsri
by
6.8k points
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