Given:
A bag has 1 orange lollipop, 2 red lollipops, 7 Green lollipops, 6 blue lollipops and 4 speckled lollipops.
To find:
The probability of getting a green and then a green.
Explanation:
Sample space
[tex]\begin{gathered} n(S)=1+2+7+6+4 \\ n(S)=20 \end{gathered}[/tex]Let A be the event of getting a green lollipop.
[tex]\begin{gathered} n(A)=7 \\ P(A)=\frac{n(A)}{n(S)} \\ =\frac{7}{20} \end{gathered}[/tex]Let B be the event of getting a green lollipop afterpout it back from the first even.
[tex]\begin{gathered} n(B)=7 \\ P(B)=\frac{7}{20} \end{gathered}[/tex]Therefore, The probability of getting a green and then a green is
[tex]\begin{gathered} P(A\cap B)=P(A)\cdot P(B) \\ =\frac{7}{20}\cdot\frac{7}{20} \\ =\frac{49}{400} \\ =0.12 \end{gathered}[/tex]