Testing if two events are independent is tough. And with a formula like P(A) = P(A|B) = P(A|not B) it can be very confusing! Our students are always messing up the conditional probabilities so they usually find the events are dependent since the probabilities are not equal.
So how can we get our students to do better with probability? This starts with a strong focus on conceptual understanding. We try to avoid formulas at all costs! When students memorize rules and formulas they don't do as well because they don't understand what they're doing. They're just replicating what they've seen.
Last year, students had the hardest time understanding how to determine if two events were independent. So this year we're going to take a little extra time to work on developing this idea with this new lesson.
Does Mrs. Gallas choke under pressure?
Activity: Does Mrs. Gallas choke under pressure?
Answer Key: PDF
In basketball, it is most common that the player shoots two consecutive free throws. Often basketball announcers will talk about how added pressure makes it more difficult to make the second shot if you miss the first shot. Mrs. Gallas thinks she is pretty good under pressure. Do her free throw stats support this? The table below shows how Mrs. Gallas performed on her second free throw shot when she was shooting two consecutive free throws.
Do you think Mrs. Gallas is affected by the pressure?