10 A box contains 15 counters.
There are 4 red counters, 5 green counters and the rest are yellow counters.

Niklas takes at random a counter from the box and writes down the colour of his counter. He then puts the counter back into the box.
Sasha then takes at random a counter from the box and writes down the colour of her counter.

Work out the probability that the counters taken by Niklas and Sasha both have the same colour.

Step 1 ：The problem is asking for the probability that both Niklas and Sasha draw the same color counter from the box. Since the counter is replaced after each draw, the probabilities do not change between draws. Therefore, the probability that they both draw the same color is the sum of the probabilities that they both draw red, both draw green, and both draw yellow.

Step 2 ：To calculate these probabilities, we need to know the total number of counters and the number of each color. We know there are 15 counters in total, 4 of which are red and 5 of which are green. The rest are yellow, so there must be 15 - 4 - 5 = 6 yellow counters.

Step 3 ：The probability of drawing a counter of a certain color is the number of counters of that color divided by the total number of counters. Therefore, the probability of both drawing red is \(\left(\frac{4}{15}\right) \times \left(\frac{4}{15}\right)\), the probability of both drawing green is \(\left(\frac{5}{15}\right) \times \left(\frac{5}{15}\right)\), and the probability of both drawing yellow is \(\left(\frac{6}{15}\right) \times \left(\frac{6}{15}\right)\).

Step 4 ：Adding these probabilities together gives us the total probability that Niklas and Sasha both draw the same color counter. This is calculated as \(\left(\frac{4}{15}\right)^2 + \left(\frac{5}{15}\right)^2 + \left(\frac{6}{15}\right)^2\).

Step 5 ：\(\boxed{\text{Final Answer: The probability that the counters taken by Niklas and Sasha both have the same colour is approximately 0.342 or 34.2%}}\).