anonymous
  • anonymous
John’s piggy bank contained 7 dimes and 3 quarters. He pulled out 1 coin without looking. Without replacing the first coin, John then pulled out a second coin. What is the probability that both coins were dimes? Express your answer in simplest form.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
My thought is that it's as simple as 2/10. Im not quite sure though.
anonymous
  • anonymous
We have two steps for this. I'll help you through them one-by-one. The first step is figuring out what the probability is for pulling the first dime out. Which is represented as \[\large \frac{no.~of~dimes}{total~no.~of~coins}\]
anonymous
  • anonymous
7/10 then I would presume?

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anonymous
  • anonymous
Yep. So our next step (3 in total, not 2 sorry) is to figure out what the probability of getting a dime would be if there is one less dime and one less coin. Which is represented as \[\large \frac{no.~of~coins~-1}{total~no.~of~coins~-1}\]
anonymous
  • anonymous
So 6/9. With the reduced dime he would have presumably pulled, it takes one away from the amount of dimes, which in return reduces the amount of coins altogether.
anonymous
  • anonymous
Right, good job. Before we move on to the final step, do you know what 6/9 will simplify to?
anonymous
  • anonymous
2/3 of course.
anonymous
  • anonymous
Great! So our final step is to multiply the two fractions together, to get the probability of both happening. So \[\large \frac{7}{10} \times \frac{2}{3}=~?\]
anonymous
  • anonymous
14/30, which would reduce to 7/15. 7 is a prime number so that must be my answer.
anonymous
  • anonymous
Cool! Thanks a lot. I appreciate your help!
anonymous
  • anonymous
Right, it would be 7/15. And also, \[\huge \color{aqua}N\color{fuchsia}o \space \color{lime}P \color{orange}r \color{blue}o \color{maroon}b \color{red}l \color{olive}e \color{purple}m \ddot\smile \]

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