Answer to Question #220259 in Statistics and Probability for Musenga sichona

Question

A bag contains 8 blue marbles, 5 yellow marbles and 2 white marbles. Two marbles are drawn from the bag, the first marble not being replaced before the second marble is drawn. What is the probability that:

i. Both marbles are the same colour

ii. Both marbles are different colours

iii. Are at least one Mable is blue

Answer 1

$$8+5+2=15$$

i.

$$P(2\ same)=\dfrac{8}{15}(\dfrac{8-1}{15-1})+(\dfrac{5}{15})(\dfrac{5-1}{15-1})$$

$$+\dfrac{2}{15}(\dfrac{2-1}{15-1})=\dfrac{78}{210}=\dfrac{13}{35}$$

ii.

$$P(2\ different)=1-P(2\ same)=1-\dfrac{13}{35}=\dfrac{22}{35}$$

iii.

$$P(at\ least\ 1B)=\dfrac{\dbinom{8}{2}\dbinom{7}{0}}{\dbinom{15}{2}}+\dfrac{\dbinom{8}{1}\dbinom{7}{1}}{\dbinom{15}{2}}$$

$$=\dfrac{28(1)}{105}+\dfrac{8(7)}{105}=\dfrac{4}{5}$$