Statistics 1

In-Class Exercise 6

Yu-You Liou

Shih Chien University

2026-09-16

Question 1

Multiplication Rule

Two cards are drawn from a standard deck of 52 cards without replacement.

1. Find the probability that both cards are hearts, using the multiplication rule for dependent events.
2. Obtain the same answer with choose().
3. Find the probability that both cards are hearts with replacement, and explain in one sentence why the two answers differ.

Question 2

Conditional Probability

A store recorded the payment method of 150 customers.

	Mobile pay	Credit card	Cash
Under 30	48	22	10
30 or over	19	35	16

1. Find the probability that a customer pays by mobile pay.
2. Find the probability that a customer pays by mobile pay given that the customer is under 30.
3. Are age group and payment method independent? Justify your answer with the two probabilities above.

Question 3

Counting Rules

Use factorial() and choose() in R.

1. A committee of 4 is chosen from 12 club members. How many different committees are possible?
2. Five of nine finalists are seated in a row on stage. How many different seating arrangements are possible?
3. From the 12 club members, in how many ways can a president, a secretary, and a treasurer be chosen? Explain in one sentence why this is a permutation rather than a combination.