Probability: These 6 coins are in a box - 10p, 10p, 10p, 20p, 20p, 50p. Someone takes 2 coins at random. What is the probability that the total value of the two coins is at least 40p?

The question has a number of important points which should be highlighted before beginning. Firstly the fact that the picks are at random. Secondly that the value of the coins must be at least 40p, so a total value of 40p is included. Also note there is no mention of the coins being replaced in the box once picked.
Possibility 1: (10p,50p) --> 3/6 x 1/5 = 1/10Possibility 2: (20p,20p) --> 1/3 x 1/5 = 1/15Possibility 3: (20p,50p) --> 1/3 x 1/5 = 1/15Possibility 4: (50p,10p) --> 1/6 x 3/5 = 1/10Possibility 5: (50p,20p) --> 1/6 x 2/5 = 1/15
The fact that the coins are not but back into the box once picked, means that the second denominator will be 5 rather that 6. It is also important to note that when the same two coins are picked to make a value, both picking orders must be included in the final answer (e.g. (10p,50p) and (50p,10p).
Then we must add all theses possibilities up:1/10 + 1/15 + 1/15 + 1/10 + 1/15 = 2/5 or 0.4It may be easier to find a common denominator so in this case the simplest common denominator is 30:3/30 + 2/30 + 2/30 + 3/30 + 2/30 = 12/30 or 0.4