The approximate probability of randomly choosing one vegetable and one grain-based side dish is: d. 0.33333
Explanation
Vegetable side dishes = 3, Fruit side dishes = 2 and Grain-based side dishes = 5
So, total number of side dishes [tex]= 3+2+5= 10[/tex]
Number of ways for choosing two side dishes from total 10 dishes will be : [tex]^1^0C_{2}[/tex]
We need to randomly choose one vegetable and one grain-based side dish, so the number of ways [tex]= ^3C_{1} * ^5C_{1}[/tex]
Thus, the probability [tex]= \frac{^3C_{1} * ^5C_{1}}{^1^0C_{2}} = \frac{3*5}{45}= \frac{15}{45}= \frac{1}{3}= 0.3333...[/tex]
