Lesson 3B: Independent & Dependent Events

 

Suppose you are at school watching a basketball game. Your favourite player is on a streak and has scored five times in a row. Which do you think is more likely on her next shot: scoring or not scoring? The common belief among basketball players and fans is that a players' probability of hitting a shot is greater following a hit than following a miss on the previous shot. However, scientific data does not support this. In fact, studies have shown that scoring is equally likely on any shot, regardless of what has occurred on previous shots. Because the result of one shot does not affect the next shot, these outcomes are examples of independent events .

In basketball, every possession of the ball is timed on a thirty-second shot clock. A team has only thirty seconds to shoot from the time they inbound the ball. If a team does not shoot the ball within thirty seconds, they lose possession of the ball.

Researchers at the University of Minnesota studied shooting patterns of National Basketball Association (NBA) players to see if they could determine an optimal time to shoot the ball in this thirty-second window. They discovered that, when significant time remains on the shot clock, players are often reluctant to shoot the ball. They wait for a better shot to arise. However, the research indicated that the opportunity for a quality shot decreases as the shot clock runs. Statistically, a player increases his or her chance of scoring by shooting soon after getting possession of the ball. If a player waits, he or she likely will miss a scoring opportunity. The players' choices of whether to shoot at early opportunities affect the team's chance of scoring.

Because the result of the players' choices affects the chances of scoring, these outcomes are examples of dependent events .

 

In this Training Camp, you will study independent and dependent events. You will learn how to identify them, and you will work with both to solve probability problems.

 

By the end of this lesson, you should be able to

	compare, using examples, dependent and independent events
	determine the probability of two dependent or two independent events
	determine the probability of an event, given the occurrence of a previous event
	solve a problem that involves determining the probability of dependent or independent events