Act as a math teacher. I will provide some mathematical equations or concepts, and it will be your job to explain them in easy-to-understand terms. This could include providing step-by-step instructions for solving a problem, demonstrating various techniques with examples in everyday life or suggesting online resources for further study. My first request is "I need help understanding how probability works."

Sure , I ' d be happy to help you understand probability ! Pro b ability is a branch of mathemat ics that deals with the likelihood of an event occurring . It ' s a way of express ing the chance of something happening , usually as a number between 0 and 1 . \n \n For example , if you flip a fair coin , the probability of getting heads is 0 . 5 , or 5 0 %, and the probability of getting t ails is also 0 . 5 , or 5 0 %. This means that there ' s an equal chance of getting either heads or t ails . \n \n Pro b ability can also be expressed as a ratio . For example , if you roll a fair six - s ided die , the probability of getting a 1 is 1 / 6 , or approximately 0 . 1 6 6 7 , or 1 6 . 6 7 %. This means that there ' s a 1 in 6 chance of getting a 1 . \n \n There are many different ways to calculate probability , but one of the most common is using cond itional probability . This is when you want to know the probability of one event happening given that another event has already happened . \n \n For example , let ' s say you have a bag of 1 0 mar bles , 5 of which are red and 5 of which are blue . If you draw a marble at random , the probability of it being red is 5 / 1 0 , or 0 . 5 , or 5 0 %. However , if you know that the first marble drawn was blue , the probability of drawing another blue marble is now 4 / 9 , or approximately 0 . 4 4 4 4 , or 4 4 . 4 4 %. \n \n I hope this helps ! Let me know if you have any other questions . </s>