According to the news, the lottery jackpot is climbing by the hour. Long lines of dreamers are forming wherever lottery tickets are sold. While you don’t usually buy lottery tickets, it is getting tempting. Just imagine what you could do with $100 million dollars. Perhaps you could retire early or never even go to work. Maybe buy a rare fancy car. All you need to do is pick the correct numbers, and the jackpot is all yours!
It sounds easy enough; just six simple numbers. But how likely are you to win? And could you increase the likelihood of winning by purchasing more lottery tickets?
To answer these questions, you need to know about permutations and combinations. So learn about them as you complete this module, and then we’ll return to the lottery at the end. Then you’ll be able to decide whether you want to stand in line to purchase a ticket.
Learning Objectives
Computing the Probability of an Event
- Describe a sample space and simple and compound events in it using standard notation
- Calculate the probability of an event using standard notation
- Calculate the probability of two independent events using standard notation
- Recognize when two events are mutually exclusive
- Calculate a conditional probability using standard notation
Applications With Probability
- Compute a conditional probability for an event
- Use Baye’s theorem to compute a conditional probability
- Calculate the expected value of an event