We have
3 red marbles
2 Blue
5 green
7 yellow
Total marbles is
T= 3+2+5+7= 17
T=17
1)Probability draws a red marble
is given by
[tex]P(r)=\frac{Red}{total}[/tex][tex]P(r)=\frac{3}{17}[/tex][tex]P(r)=\frac{3}{17}=0.1764[/tex]
2)Draws yellow replace it then draws blue
Draws yellow probability is given by
[tex]P(y)=\frac{7}{17}[/tex]
when the text says replace it means we have the same total number of marbles
Draws blue probability is given by
[tex]P(b)=\frac{2}{17}[/tex]
then the probability of Draws yellow replace it then draws blue is
[tex]P(yb)=P(y)*p(b)[/tex][tex]P(yb)=\frac{7}{17}*\frac{2}{17}[/tex][tex]P(yb)=\frac{14}{289}=0.048[/tex]
c)Draws blue marble, does not replace it then draws green marble
probability of draws blue
[tex]P(b)=\frac{2}{17}[/tex]
since we do not replace the marble the new total of marbles is 16
then
the probability of draw a green is
[tex]p(g)=\frac{5}{16}[/tex]
then
Draws blue marble, does not replace it then draws green marble
[tex]p(bg)=p(b)*p(g)[/tex][tex]p(bg)=\frac{5}{136}=0.036[/tex]
