Paul an Peter each toss a coin and record the results.

Paul:
H H T H T H H H T T H H T H T H T H H T T

Peter:
H T H H T H H T T H T H ... ...

If the probability of heads to tails was the same for both boys, what were peter's last two tosses?

To determine Peter's last two tosses, we need to analyze the given information and find a pattern in his coin tosses.

Let's look at Paul's tosses first:

H H T H T H H H T T H H T H T H T H H T T

Counting the number of heads (H) and tails (T) in Paul's tosses, we have:
Heads: 14
Tails: 8

Since the probability of heads and tails is the same for both boys, we can assume that Peter also has a ratio of approximately 14 heads to 8 tails in his tosses.

Now let's look at Peter's tosses:

H T H H T H H T T H T H ...

We can continue the pattern of Peter's tosses by balancing the ratio of heads and tails. Since Peter needs 14 heads and 8 tails in total, let's add up the known tosses:

H T H H T H H T T H T H ...

Heads: 8
Tails: 4

To reach a total of 14 heads, Peter needs 14 - 8 = 6 more heads. Similarly, he needs 8 - 4 = 4 more tails.

Adding 6 more heads, we get:
... H H H H H H

Adding 4 more tails, we get:
... T T T T

Therefore, Peter's last two tosses are: H H T T T T.