5.104 Streak shooter Sportscaster Maria Coselli claims that players on the New York Knicks professional basketball team are streak shooters. To make her case, she looks at the statistics for all the team’s players over the past three games and points out that one of them (Joe Smith)

made six shots in a row at one stage. Coselli argues,

“Over a season, Smith makes only 45% of his shots. The probability that he would make six in a row if the shots were independent is 10.4526 = 0.008, less than one in a hundred. This would be such an unusual occurrence that we can conclude that Smith is a streak shooter.”

a. Explain the flaws in Coselli’s logic.

b. Use this example to explain how some things that look highly coincidental may not be so when viewed in a wider context.