Chapter 5.2, Problem 34E

(a)

To determine

Discuss the probability model for the chance process.

Answer to Problem 34E

All possible combinations:

Abigail − Bobby

Abigail − Carlos

Abigail − DeAnna

Abigail − Emily

Bobby − Carlos

Bobby − DeAnna

Bobby − Emily

Carlos − DeAnna

Carlos − Emily

DeAnna − Emily

Explanation of Solution

Given information:

5 people are:

Abigail, Bobby, DeAnna, Emily, Carlos.

Every time, 2 people are randomly picked to pay for lunch.

When names are drawn from a hat, 2 people are randomly picked to pay for the lunch.

For making all possible combinations:

First name is paired with 4 other names.

Second name is paired with remaining 3 names.

Third name is paired with remaining 2 names.

Fourth name is paired with remaining last name.

Thus,

All possible combinations (2 of the 5 people are randomly picked):

Abigail − Bobby

Abigail − Carlos

Abigail − DeAnna

Abigail − Emily

Bobby − Carlos

Bobby − DeAnna

Bobby − Emily

Carlos − DeAnna

Carlos − Emily

DeAnna − Emily

Note that

Since 2 people are randomly picked from the group, the order of combinations does not matter.

(b)

To determine

Probability for Carlos or DeAnna (or both) ends up paying for lunch.

Answer to Problem 34E

Probability,

  $P\left(\text{Carlos}\text{or}\text{DeAnna}\text{or}\text{both}\right)=0.7$

Explanation of Solution

Given information:

5 people are:

Abigail, Bobby, DeAnna, Emily, Carlos.

Every time, 2 people are randomly picked to pay for lunch.

Note that

Name of Carlos or DeAnna (or both) is mentioned in 7 of 10 possible combinations (see Part (a)).

Now,

When the number of favorable outcomes is divided by the number of possible outcomes, we get the probability.

  $P\left(\text{Carlos}\text{or}\text{DeAnna}\text{or}\text{both}\right)=\frac{\text{Number}\text{of}\text{favourable}\text{outcomes}}{\text{Number}\text{of}\text{possible}\text{outcomes}}=\frac{7}{10}=0.7=70\%$

Thus,

The probability that Carlos or DeAnna (or both) ends up paying for lunch is 0.70.