A bag contains #10# red and # 6# black cubes. Take any random cube from the bag and do not replace it. Then we draw another cube and we do not put it back in the bag. Calculate the probability that ?

a) - both cubes are red in color
- both cubes are black
-cubes have different colors

A third cube was selected

b) Calculate the probability that all cubes extracted from the bags will have the same color

1 Answer
May 2, 2018

#P(R,R)=3/8#
#P(B,B)=1/2#
#P("different")=1/2#

Explanation:

There are #16# cubes in the bag. When one is taken out there will be #15# cubes in the bag.

a) When two cubes are taken out:
- The probability that both are Red:

#P(R,R) = P(R)xxP(R)#

#= 10/16 xx9/15 = 3/8#

The total number of cubes and the number of Red cubes decrease.

  • the probability that both are Black:

#P(B,B) = P(B) xx P(B)#

#= 6/16 xx5/15 = 1/8#

  • the probability that they are different colours:

#P(B,R) or P(R,B) = P(B)xxP(R) + P(R) xx P(B)#

#=10/16 xx 6/15 +6/16 xx 10/15#

#=1/4 +1/4#

#=1/2#

Note the sum of the probabilities:

#3/8+1/8+1/2 = 1#

b) Three cubes are taken.

The probability that they are all the same colour:

#P(R,R,R) or P(B,B,B)#

#=(10/16 xx 9/15 xx 8/14) + (6/16 xx5/15xx4/14)#

#= 3/14 +1/28#

#=1/4#