Given:
It is given that
Probability of winning $ 0 =
![(3)/(10)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/5wqijkf04vjcwyrmczjosx8b5pafrel3pm.png)
Probability of winning $ 100 =
![(1)/(5)](https://img.qammunity.org/2021/formulas/mathematics/high-school/nve42zwxkm2ttkh80stksgu37lazt1jlhm.png)
Probability of winning $ 200 =
![(1)/(10)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/aepwrh3e943x7efcio9xavy7vrbdkbcn1i.png)
Probability of winning $ 500 =
![(2)/(5)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/5jm6oitkd3lorjig5jfw17qliocw7lqrpz.png)
To find the probability of not winning a cash prize.
Step-by-step explanation:
Not winning cash prize = winning $ 0
So,
Probability of not winning a cash prize
= Probability of winning $ 0
=
![(3)/(10)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/5wqijkf04vjcwyrmczjosx8b5pafrel3pm.png)
Therefore,
The probability of not winning a cash prize is
. Option D.