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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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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Answer 1 · 2017-05-22T15:11:24

$14/45$

Explanation:

$"assuming no replacement"$

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

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

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

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

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

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

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

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

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

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

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

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

$=14/45$

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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?

1 Answer

Explanation:

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