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We need to give probability model for this chance process.

We are given five peoples Abigail, Bobby, Carlos, DeAnna, and Emily . We have to pick two people randomly from hat to pay for lunch.

So we need to find all possible combination and order of name doesnot matter.

Therefore,

Abigail - Bobby
Abigail - Carlos
Abigail - DeAnna
Abigail - Emily
Bobby - Carlos
Bobby - DeAnna
Bobby - Emily
Carlos - DeAnna
Carlos - Emily
DeAnna-Emily

We need to find probability if Carlos or DeAnna (or both) ends up paying for lunch.

We are given five peoples Abigail, Bobby, Carlos, DeAnna, and Emily . We have to pick two people Carlos or DeAnna (or both) from hat so to pay for lunch.

Carlos or DeAnna have sevel possible outcomes :
Abigail - Carlos
Abigail - DeAnna
Bobby - Carlos
Bobby - DeAnna
Carlos - DeAnna
Carlos - Emily
DeAnna-Emily

$\mathrm{P}(\mathrm{Carlos}\mathrm{or}\mathrm{DeAnna}\mathrm{or}\mathrm{both})=\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{cases}}{\mathrm{Number}\mathrm{of}\mathrm{possible}\mathrm{cases}}=\frac{7}{10}=0.7$

Probability that Carlos or DeAnna (or both) ends up paying for lunch is$0.7$