Probability - Question

Question

Hotel A and B offers 2 types of packages that include lodging only or lodging with breakfast. From a group of 300 tourists, 30 tourist choose Hotel A for lodging only and 120 tourists choose Hotel B for lodging with breakfast. Altogether 110 tourists choose to stay in Hotel A. A tourist is selected randomly;

What is the probability that the tourist chooses Hotel A or tourists chooses lodging only?

What is the probability that the tourist to choose Hotel B for lodging with breakfast, if he chose Hotel B?

Answer 1

I have found that the most helpful way to these types of problems is to create a table as shown below. On one side, you have Hotel A and Hotel B. On the other side, you have Lodge Only and Lodge and Breakfast. By filling in each piece of the table, outlined below, it makes finding the various probabilities easier to visualize.

Lodge Only Lodge / Breakfast Total

Hotel A 30 y 110

Hotel B x 120 190 (if there's 110 for Hotel A and 300 total, 190 for B)

Total 30+x 120+y 300

30 + y = 110

y = 80 - stay in hotel A for lodge / breakfast

x+120 = 190

x = 70 - stay in hotel B for lodge only

Let's fill in the rest of the table

Lodge Only Lodge / Breakfast Total

Hotel A 30 80 110

Hotel B 70 120 190

Total 100 200 300

# of people choosing hotel A = 110

# of people choosing lodging only = 100

# of people who overlap between these 2 groups = 30 (Hotel A and Lodge Only)

Therefore, probability of choosing Hotel A or lodging only = (110+100-30) / 300

60.0%

# of people choosing Hotel B for lodging / breakfast = 120

# of people choosing hotel B = 190

probability = 120/190

63.2%