Button jar contains 5 red buttons, 3 blue buttons, 1 green button and 1 yellow button. What is the probability that if I reach in and pull out a button randomly, it will be blue? Using the same jar, with 5 red buttons, 3 blue buttons, 1 green button and 1 yellow button. I pull out 1 button, replace it and shake the jar, and pull out a second button. What is the possibility that neither button is red?

First we need to calculate how many buttons there are. There are 10 buttons. So the probability of getting a blue one is 3/10 for 3 buttons. So that means that the answer to the first one is 30%. So if we get that neither is red  we know that the probability of getting a red one is 5/10. So there is a 50% chance of getting a red button and 50% of not. Then we multiply them 5/10*5/10 for 2 times. we get 25/100 aka 25%. So the answer to this question is 25%.

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It's in the picture, desmos will help for graphing.