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Note the following rules for simultaneous equations: 'Same sign subtract' and 'alternate sign add'. The first thing we need to do is find either y or x. To do so here, you add the equations together becau...

Let x = 0.436363636...
10x = 4.36363636....1000x = 436.36363636...990x = 432x = 432/990 = 24/55

The chances of Alice winning a game is 0.7, therefore the chances of Bob winning a game is 0.3. To work out the probability of Alice winning exactly one game, the probabilities of Alice winning once and B...

We first need to simplify both the numerator and denominator of this fraction seperately. Let's start with the numerator: x^2 -2x -15We need to find two numbers that add to make -2 and multip...