a Divide the number of favorable outcomes with the number of possible outcomes. Remember, we are only considering people going on a business trip.
B
b Compare P(Laptop) and P(Laptop|Business trip).
A
a 46 %
B
b Yes, they are associated.
Practice makes perfect
a To calculate probability we divide the number of favorable outcomes with the number of possible outcomes.
P=Number of favorable outcomes/Number of possible outcomes
Given that someone is traveling for business the number of possible outcomes is 236+274=510. From the table, we see that 236 people travel with a laptop. With this information, we can calculate the conditional probability.
P(Laptop|Business trip)=236/510≈ 46 %
About 46 % of the people traveling for business do it with a laptop.
b If the events are associated, the probability of having a computer is affected by a person's reasons for traveling.
From Part A, we know that about 46 % of people traveling for business bring a computer. To determine if there is an association, we should also calculate the general probability of someone traveling and bringing a computer.
P(Laptop)=236+93/1000≈ 32.9 %
About 32.9 % of the people traveling bring a laptop. Since the conditional probability of bringing a laptop given a business trip is different from the probability of bringing a laptop overall, the events are associated.
