1.
A box contains three marbles, one red (R), one green (G), and one blue (B). A first marble is
chosen, its color is recorded, and then it is replaced in the box and a second marble is chosen,
and its color is recorded. Find the sample space.
{(R, R), (R, G), (R, B), (G, R), (G, G), (G, B), (B, R), (B, G), (B, B)}
{(R, G), (R, B), (G, R), (G, B), (B, R), (B, G)}
{(R, B), (B, G), (G, R)}
{R, G, B}
Sample space =>
{(R,R), (R,G), (R,B), (G,R), (G,G), (G,B), (B,R), (B,B), (B,G)} i.e. 9
Sample space =>
not replaced => same color will not be there
i.e.
{(R,G), (R,B), (G,R), (G,B), (B,R), (B,G)}
i.e. 6
2.
If a committee of
3
is to be chosen at random from a class of
10
students, what is the probability of
any particular committee being selected? (Enter your answer as a fraction.)
Probability of an event,
P
(
E
)
=
n
(
E
)
n
(
S
)
n(S) = total number of outcomes in sample space S.
n(S) =
10
C
3
=
(
n!
)
r!
(
n
−
r
)
!
=
10
!
3
!
(
10
−
3
)
!
=
3628800
(
30240
)
=
1
20
n(E) = number of outcomes in the event E = 1
P
(
E
)
=
n
(
E
)
n
(
S
)
=
1
120
What if the committee is to consist of a president, a vice president, and a treasurer? (Enter your answer
mc
RN_1633648_1_0
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