Who’s paying? Abigail, Bobby, Carlos, DeAnna, and Emily go to the bagel shop for lunch every Thursday. Each time, they randomly pick $2$of the group to pay for lunch by drawing names from a hat.

a. Give a probability model for this chance process.

b. Find the probability that Carlos or DeAnna (or both) ends up paying for lunch.

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$0.7$