Stats and probability in Mathematics is often used for recording and forecasting. The stats themselves are more recorded for reference, while the probability or likelihood is more for forecasting. So, let us first consider statistics.
Statistics really refers to recorded stats. Stats are widely used, as for example in sports such as golf and soccer. In the game of golf, scores are kept over 9 or 18 holes. When complete, stats from these scores can include a stroke average per hole or a putting average which can the be recorded and compared. Alternatively, in the game of soccer game stats can include shots at goal by both teams, number of corners taken or perhaps the percentage share of possession. This will indicate which team has had the better of the game.
Such statistics can be recorded in a variety of ways. Although, most notably stats can often include mode, median or mean averages. The mode is simply the most recurring number from a range. The median is a middle value in a range. Then the mean average, totals a range of numbers and then divides by how many were included, which is good for stroke averages in golf.
With regard to probability, this is really a reference to the likelihood of eventual outcomes. This is used more for forecasting models, and is sometimes considered as a percentage outcome. Where forecasts have to be made, probability can sometimes be referred to.
As such, fractions and percentages are often referred to with regard to probability. To find a percentage, the number one is divided by the potential number of outcomes. Then, to convert to percentage it can be multiplied by 100. A good example would be flicking a coin. A coin has head or tails, so 1 is divided by 2 which gives 0.5. When multiplied by 100 0.5 becomes 50%. So, the statistical probability of the coin landing on either heads or tails is 50% which is exactly equal.
So, for any forecasting the probability can be referred to as such. Let us say for example a game of Roulette, where you cover 24 of the numbers on the table. Your statistical chance of winning is then divided by the 37 numbers of the table, which gives 0.64 or 64%. As such, with a 64% chance of the ball landing on your number it is likey that it will. Playing this, you will certainly hit more numbers. Another example would be rolling a dice, with one in six outcomes it is unlikely you will roll on a six!
As such, stats are used more for reference and records. Probability is more of a forecast, or a statistical chance. For sport’s predictions stats may be better, while probability is a percentage forecast.