3. (a) Hold a penny upright on its edge under your forefinger on a hard surface, and then snap it with your other forefinger so that it spins for some time before falling. Based on 50 spins, estimate the probability of heads.
(b) Toss a thumbtack with a gently curved back (similar to Figure 8.4, page 344) on a hard surface 100 times. (To speed up the process, toss 10 at a time.) How many times did it land with the point up? What is the approximate probability of landing point up?
3.
(a) Results will vary, but the probability of a head is usually greater than 0.5 when spinning pennies. One possible explanation is the “bottle cap effect.” The rim on a penny is slightly wider on the head side, so just as spinning bottle caps almost always fall with the open side up, pennies fall more often with the head side up. Additional results will vary.
(b) Sample response: In 54 of the 100 tosses, the tack landed point up. Hence, the estimated probability is 0.54.