Question

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.

Short answer

Part(a) Probability model is all possible combinations:
Abigail - Bobby
Abigail - Carlos
Abigail - DeAnna
Abigail - Emily
Bobby - Carlos
Bobby - DeAnna
Bobby - Emily
Carlos - DeAnna
Carlos - Emily
DeAnna-Emily

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

Step-by-step solution

Part(a) Step 1 : Given information

We need to give probability model for this chance process.

Part(a) Step 2 : Simplify

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

Part(b) Step 1 : Given information

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

Part(b) Step 2 : Simplify

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$0.7$