Question 1139892
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The solution by tutor @ikleyn is a perfectly good solution using basic ideas of probability.<br>
You should understand that method and know how to use it.<br>
Here is a solution by a different method that is bit more difficult than her method for this problem but can be an easier method to use when similar problems get more difficult.<br>
You should also understand and be able to use this method for similar problems.<br>
The total number of ways of choosing 2 of the 50 coins in the box is "50 choose 2"; the number of ways of choosing 2 of the 15 quarters is "15 choose 2".  The probability of getting 2 quarters when 2 coins are randomly drawn from the box is<br>
{{{C(15,2)/C(50,2)}}}<br>
{{{C(50,2) = (50*49)/(2*1) = 25*49 = 1225}}}
{{{C(15,2) = (15*14)/(2*1) = 15*7 = 105}}}<br>
Then the probability is<br>
{{{105/1225 = 3/35}}}