Answer: [tex]\dfrac{7}{145}[/tex] .
Step-by-step explanation:
Given ,The bag contains :
9 chocolate chip cookies, 5 peanut butter cookies, 9 sugar cookies and 7 oatmeal raisin cookies.
Total cookies = 9+5+9+7=30
Now , the number of ways to choose any two cookies ( one after another) :
[tex]^{30}C_2=\dfrac{30!}{2!(30-2)!}=\dfrac{30\times29\times28!}{2\times28!}=435[/tex]
The number of way to choose two oatmeal raisins ( one after another) :
[tex]^{7}C_2=\dfrac{7!}{2!(7-2)!}=\dfrac{7\times6\times5!}{2\times5!}=21[/tex]
Now , the probability that Skyler randomly selects an oatmeal raisin cookie from the bag, eats it, then randomly selects another oatmeal raisin cookie will be :
[tex]\dfrac{21}{435}=\dfrac{7}{145}[/tex]
Hence, the required probability is [tex]\dfrac{7}{145}[/tex] .
