Question

When a basketball player makes a trip to the free throw line, he takes two consecutive shots. It is often wondered
whether these two shots are independent or dependent: does the probability of making the second free throw depend
on whether a player makes the first free throw?
After analyzing data for Lebron James, statisticians determined that his first and second free throws are entirely
independent events. The frequency table below shows the data that analysts used to determine this independence.

Answer 1

Answer:

• 144
• 36
• 48
• 12

Step-by-step explanation:

Since the shots are independent, they have the same ratio across the row and down the column as the totals have. Ratios in the same row are 3:1; ratios in the same column are 4:1.

(1st shot, 2nd shot) = (makes, makes) = 144

  = (makes, misses) = 180-144 = 36

  = (misses, makes) = 192-144 = 48

  = (misses, misses) = 60-48 = 12