Question

Jan's hypothesis H is that her car needs a new transmission belt, and the potential evidence E is that her mechanic has said that it probably does. Which of the following cases would be a case where observing E would count as evidence in favour of H?

	P(E) = 57% and P(H) = 47%
	P(H given E) = 57% and P(E given H) = 47%
	P(H) = 57% and P(H given E) = 47%
	P(H given E) = 57% and P(H) = 47%

Say we have two events A and B and we know the probability that they occur is P(A) = 0.4 and P(B) = 0.2 respectively. What condition must be satisfied in order to say that the probability that either A or B occurs is 0.6?

	The probabilities must be related.
	The probabilities must be less than one.
	The events should not both be able to happen at the same time.
	The probabilities must be independent

Match each of the scenarios with the definition of probability it relies on:

123	You decide that you have a 95% chance of passing this unit.
123	Collect 283 Pokemon of which 97 are Zubats. Assume that the probability a random Pokemon is a Zubat is 97/283.
123	Toss a fair coin. Assume the probability of it coming up Tails is 50%.

1.	Long run frequency interpretation.
2.	Equally likely outcomes.
3.	Subjective probability.

Answer 1

Problem 1: P(H given E) = 57% and P(E given H) = 47%

Problem 2: P(A or B)=P(A)+P(B)-P(A and B)=0.6

or, P(A and B)=0.6-0.6=0 (since P(A)=0.4, P(B)=0.2)

Hence A and B are mutually exclusive.

Option: The events should not both be able to happen at the same time.

Problem 3:

You decide that you have a 95% chance of passing this unit	3. Subjective probability
Collect 283 Pokemon of which 97 are Zubats. Assume that the probability a random Pokemon is a Zubat is 97/283	2. Equally likely outcomes
Toss a fair coin. Assume the probability of it coming up Tails is 50%	1. Long run frequency interpretation.