# There are 5 red pens, 3 blue pens and 2 green pens in a box. Gary takes at random a pen from the box and gives the pen to his friend. He then takes at random another pen the box. What's the probability that both pens are the same colour?

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Jim G.
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May 22, 2017

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#"assuming no replacement"#

#"total number of pens "=5+3+2=10#

#P(color(red)"red")=5/10=1/2#

#P("another"color(red)" red")=4/9#

#rArrP(color(red)"2 reds")=1/2xx4/9=2/9#

#P(color(blue)"blue")=3/10#

#P("another "color(blue)"blue")=2/9#

#rArrP(color(blue)"2 blues")=3/10xx2/9=1/15#

#P(color(green)"green")=2/10=1/5#

#P("another "color(green)"green")=1/9#

#P(color(green)"2 greens")=1/5xx1/9=1/45#

#rArrP(color(red)"2 reds")" or " P(color(blue)"2 blues")" or " P(color(green)"2 greens")#

#=2/9+1/15+1/45#

#=14/45#

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