Question

The game described in Question 6 has a final level in which the player’s avatar fires a paint bomb at a series of 5 moving targets. The developers estimate that an experienced player will have a 35% chance of hitting any given target and that the chance of success with each target will be independent of the results for other attempts.

Let ? be the number of times the target is hit out of 5 attempts. Answer the following questions about this scenario.

(a) What is the distribution of ?? Include the values of any relevant parameters.

(b) How many times would you expect an experienced player to hit this target out of the 5 attempts? (That is, what is the expected value E(?)?)

(c) What is the probability that an experienced player will hit the target at least once in the 5 attempts?

(d) The developers would like to decrease the probability from part (c) to 75% by adjusting the estimated success rate for the player on an individual target. To what value should they adjust this success rate in order to achieve this goal?

Answer 1