Question

The following table summarizes endothermic reactions involving sodium bicarbonate.

Temperature in K	Heat Absorbed (Calories)
	Below Target	Above Target
266	8	40
271	44	16
274	56	36

Let A denote the event that a reaction's final temperature is 271 K or more. Let B denote the event that the heat absorbed is below target.

a) What is P(A intersection B)? Please report your answer in 3 decimal places.

b) Are events A and B mutually exclusive?

Answer 1

Answer a)

No. of endothermic reactions with final temp. 271K or more & in which heat absorbed is below target = 44+56

No. of endothermic reactions with final temp. 271K or more & in which heat absorbed is below target = 100

Total no. of endothermic reactions studied = 200

P(A intersection B) = No. of endothermic reactions with final temp. 271K or more & in which heat absorbed is below target/Total no. of endothermic reactions studied

P(A intersection B) = 100/200

P(A intersection B) = 0.500

Answer b)

Two events A and B are said to be mutually exclusive if P(A intersection B) = 0

In this case, P(A intersection B) ≠ 0, so events are not mutually exclusive.

The events A and B are not mutually exclusive