Question #dfd04

1 Answer
EZ as pi
Feb 17, 2017

a)#P("same") = 17/55#

b)#P("at least 1 red") = 8/11#

Explanation:

There are 11 balls in the container, but once one has been taken out there are only 10 left. This means that the probabilities for the first and second balls are different.

a) For the balls to be the same color there are 3 ways it can happen:

Both are blue, OR both are white, OR both are red.

#P("same") = P(BB)+P(WW)+P(R R)#

#P("same")=2/11xx1/10 + 4/11xx3/10 + 5/11xx4/10#

#P("same") =2/110+12/110+20/110= 34/110#

#P("same") = 17/55#

b) To have at least one red ball, there are three possibilities:
(Remember 5 are red and 6 are not)

The first is red and the second is not, OR the first is not but the second one is red, OR they are BOTH red.

#P("at least 1 red") = P(RN)+P(NR)+P(R R)#

#P("at least 1 red") = 5/11xx6/10+ 6/11 xx 5/10 +5/11xx4/10#

#P("at least 1 red") = 30/110 +30/110+20/110 = 80/110#

#P("at least 1 red") = 8/11#

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