Question

A jar contains two blue and five green marbles. A marble is drawn at random and then replaced. A second marble drawn at random. For each of the following, find the probability that: a) both marbles are blue b) both marbles are the same color the marbles are different in color

Answer 1

corrected question:A jar contains two blue and five green marbles. A marble is drawn at random and then replaced. A second marble drawn at random. For each of the following, find the probability that: a) both marbles are blue b) both marbles are the same color c)the marbles are different in color

Answer:

Explanation:

The probability was done with replacement.

Probaility of an event happening
`=(number of required outcomes)/(number of possible outcomes)`

number of blue marbles= 2

number of green marbles=5

total number of marbles=7

(a) probability that both marbles are blue = pr(first is blue)*pr(second is blue)

`=(2)/(7)*(2)/(7)`

`=(4)/(49)`

(b)probability that both marbles are the same color =pr(first is blue)*pr(second is blue) + Pr(first is green)*Pr(second is green)

`=(4)/(49) + (5)/(7)*(5)/(7)`

`=(4)/(49) + (25)/(49)`

`=(29)/(49)`

(c)Probability that the marbles are different in colors=pr(first is blue)*pr(second is green) + Pr(first is green)*Pr(second is blue)

`=(2)/(7)*(5)/(7)+ (5)/(7)*(2)/(7)`

`=(10)/(49)+(10)/(49)`

`=(20)/(49)`