Guided Example #1 - Probability: Introduction

A student goes to a coffee shop every day. The probability that she orders a hot drink is 0.40, and the probability that she orders a pastry is 0.30. The probability that she orders a pastry with a hot drink is 0.20. What is the probability that the student orders a hot drink, pastry, or both?

A. $0.12$ B. $0.70$ C. $0.50$ D. $0.80$

Step 1

Let F = the event that the student orders a hot drink; and let E = the event that the student orders a pastry. Then, based on the rule of addition:

$P (F ⋃ E) = P (F) + P (E) - P (F ⋂ E)$ .

Step 2

$P (F ⋃ E) = 0.40 + 0.30 - 0.20 = 0.50$ .

All Steps

Let F = the event that the student orders a hot drink; and let E = the event that the student orders a pastry. Then, based on the rule of addition:

$P (F ⋃ E) = P (F) + P (E) - P (F ⋂ E)$ .

$P (F ⋃ E) = 0.40 + 0.30 - 0.20 = 0.50$ .