Question

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).

Answer 1

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