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:

Step-by-step explanation:

The probability was done with replacement.

Probaility of an event happening$=\frac{number of required outcomes}{number of possible outcomes}$

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)

                                  $=\frac{2}{7}*\frac{2}{7}$

                                   $=\frac{4}{49}$

(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)

   $=\frac{4}{49} + \frac{5}{7}*\frac{5}{7}$

   $=\frac{4}{49} + \frac{25}{49}$

 $=\frac{29}{49}$

(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)

  $=\frac{2}{7}*\frac{5}{7}+ \frac{5}{7}*\frac{2}{7}$

           $=\frac{10}{49}+\frac{10}{49}$

      $=\frac{20}{49}$