Question

In a box there are 4 blue and 8 white marbles. If 2 marables are selected at random, what is the probability to see

a, marbles of the same color?

b, marbles of different color?

c, both blue marbles ?

d, both white marbles?

Answer 1

There are $4+8=12$ marbles.

$$S=\{BB, BW, WB, WW\}$$

a)

$$P(2\ same \ color)=P(BB)+P(WW)$$

$$=\dfrac{4}{12}(\dfrac{4-1}{12-1})+\dfrac{8}{12}(\dfrac{8-1}{12-1})=\dfrac{17}{33}$$

b)

$$P(2\ different \ color)=P(BW)+P(WB)$$

$$=\dfrac{4}{12}(\dfrac{8}{12-1})+\dfrac{8}{12}(\dfrac{4}{12-1})=\dfrac{16}{33}$$

$$=1-P(2\ same \ color)$$

c)

$$P(BB)=\dfrac{4}{12}(\dfrac{4-1}{12-1})=\dfrac{1}{11}$$

d)

$$P(WW)=\dfrac{8}{12}(\dfrac{8-1}{12-1})=\dfrac{14}{33}$$