# Oxford PAT 2015, Question 6

## 6 thoughts on “Oxford PAT 2015, Question 6”

1. For part b I interpreted two consecutive toss results being the same as being all of the outcomes where there are two, or three consecutive tosses being the same, of which there are six in total, leading to a probability of 3/4. This is because surely if you toss a coin three times and get three tails or three heads you would count that as fulfilling the criteria of having two consecutive heads or to consecutive tails?

1. Yes this is the same as the comment below. Part b implies 8 outcomes, 6 of which satisfy the condition, which is ‘are either 1 and 2 the same or 2 and 3 the same’ (when the coin tosses are numbered 1, 2 and 3).

2. Part b says:

For part b, I don’t think you count T T T twice as that doesn’t double the probability

1. That is an interesting point.

I have interpreted the question in (b) as saying that each triple coin toss contains two outcomes (“are 1 and 2 the same”, and “are 2 and 3 the same”) and counted up a total of 16 possible outcomes, 8 of which are ‘yes’. I think you are saying that each triple coin toss should be one outcome corresponding to the question ‘are either 1 and 2 the same or 2 and 3 the same’, for a total of 8 outcomes, 6 of which are ‘yes’.

I expect you’re probably right that your interpretation is the one that was intended.

1. See the comment titled ‘Part b’ above. I think actually the number of outcomes should be 8 and the probability we are looking for is the probability that either the first and second tosses are the same or the second and third tosses are the same.