Home > Statistics > Basic Probability Concepts

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?

Answer 1

Emery Adams

#14/45#

#"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#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.