Question

1. The following table summarize 200 endothermic reactions involving sodium bicarbonate. Heat Absorbed (cal) Below Target (B) Above target (B') Final Temperature Conditions Final Temperature "266 K" Final Temperature .271 K" Final Temperature "274 K" 12 42 54 40 16 36 Note that the total number of reactions in this table is 12 + 40 +42 + 16 +54 + 36 -200, and below we consider two different eventS Let A denote the event that a reaction's final temperature is 271K or less (i.e., the first two rows). Let B denote the event that the heat absorbed in a reaction is below target (i.e., the first column) (i) Determine the number of reactions in each of the following events. (a) A (b) B (c) An B (d) A' (e) AUB (f) AUB'(g) A'n B' (ii) Determine the following probabilities. (a) P(A) (b) P(B) (c) P(AnB) (d) P(A') (e) P(AU B) (f) P(AUB') (g) P(A'nB')

Answer 1

i)

(a)

Number of reactions in A is

12+40+42+16=110

(b)

Number of reactions in B is

12+42+54=108

(c)

Number of reactions in A $\cap$ B is

12+42=54

(d)

Number of reactions in A` is

200-110=90

(e)

Number of reactions in A $\cup$ B is

A $\cup$ B= A + B - A $\cap$ B

=110+108-54= 164

(f)

Number of reactions in A $\cup$ B` is

A $\cup$ B`= A + B` - A $\cap$ B`

=110+92-56= 146

(g)

Number of reactions in A` $\cap$ B` is

=36

(ii)

(a)

The probability of A is

110/200=0.55

(b)

The probability of B is

108/200=0.54

(c)

The probability of A $\cap$ B is

54/200=0.27

(d)

The probability of A` is

90/200=0.45

(e)

The probability of A $\cup$ B is

164/200=0.82

(f)

The probability of A $\cup$ B` is

146/200=0.73

(g)

The probability of  A` $\cap$ B` is

=36/200=0.18