Question

(5 pts each) A basketball player is fouled while attempting a shot for 2 points. If they make the shot, they shoot one free throw for one additional point. If they miss the shot, they shoot two free throws for one point each. Suppose the player has a 20% chance of making the shot and a 65% chance of making each free throw. • (1) Draw a Tree Diagram for this experiment. • (2) What is the probability that the player earns at least 2 points from this fouled shoot? What are the criteria for an experiment to be binomial? Does the experiment of making shots in Problem #12 satisfy all of them?

Answer 1

Ans':- 1. Tree diagram is as follows.- makes free Throw 65 (3 points) does not make free T. 35 (2 points) (1 pt) makes the shot does not makeshot and Throw does nol- 95 st 2nd Throw makes (2 pts) 65 '8 1 Throw makes 65 ist Throw doesn't .35 and Throw does not '35 (opts) (18+) 2had Throw makes 65 2. Platleast 2 pts) =P(Point =2) + PC Point = 3) = 2 X'35 + 8x 65 x 65 + '2*'65 0.538

Criteria to be Binomial distribution. 1. Fixed number of fruials. 2. Each trial is independent of others. 3. Only 2 outcomes. 4. Probability of each outcome remains constant Since in this experiment probability of success ie probability of a successful throw is not same so this CANNOT be modeled as Binomial.