Probability (Multiple Events: And vs. Or)

State whether the following questions are AND or OR probabilities and if adding the additional conditions will raise or lower the probability. (Note, for practice you can calculate most of these probabilities, but some of the AND probabilities are a little complicated because there is some overlap between the conditions, which is unknown, and which you would typically need to subtract out.)

A local animal shelter knows that the probability that someone who walks into the shelter will adopt a dog is 10% and the probability that someone who walks into the shelter will adopt a cat is 12%.  The probability that someone who walks into the shelter will adopt a rabbit, bird, or other animal is 2%.  

1.  What is the probabilty that someone adopts a dog and a hamster?

2.  What is the probability that someone adopts a dog or a cat?

3.  What is the probability that someone adopts a dog, cat, and a bird?

4.  What is the probability that someone adopts any animal at all?

A fast food restaurant, Texan Burger, is famous for its signature BBQ burger and 60% of customers order a BBQ burger whenever they come in. They also make great fries and 80% of customers order fries when they eat.  Nearly 90% of customers order a soft drink whenever they eat at Texan Burger.  Just under 15% of customers get a kids meal and 20% of customers order some kind of chicken dish.

5.  What is the probability of a customer ordering a chicken dish or a kids meal?

6.  What is the probability of a customer ordering a drink and not a BBQ burger?

7.  What is the probability of a customer ordering a BBQ burger and either a drink or fries?

8.  What is the probability of a customer ordering neither fries nor a drink?

Mariana is learning to play poker.  She knows that there are 52 cards in a deck, 4 cards of each type, 13 cards of each suit (e.g., each deck contains 4 kings, 4 queens, and 4 sevens as well as 13 hearts, 13 spades, etc.). She knows that pairs (e.g., 2 aces, 2 eights) are good, but that flushes (all five cards the same suit -- e.g., all five cards are hearts or diamonds) are better.  She knows that straights (all 5 cards going in order: 2, 3, 4, 5, 6) are even better.  She wants to win!

9. Her first four cards are a 5, a 7, a jack, and an ace.  What is the probability that her fifth card will be a pair with one of her first four cards?  

10. She really wants either a jack or a heart.  What is the probability that she'll get either one?

11.  What is the probability that she'll get a jack of hearts?

12.  What is the probablity that she'll get a card that is neither a jack or a heart?