Unit 5 - Activity 3 - Geometric Distribution Worksheete Geometric distribution is a probability model that helps us determine how many failures occur before a single success.~ Random Variable, x = number of failures before successe Probability in a geometric Distribution: P(x) = q*pu q = probability of failure for a single trial p = probability of success for a single trial x = number of failures p + q = le Expectation of a Geometric Distribution: CO E(x) = > xp (x)+ *=0 E(x) = p q = probability of failure for a single trial p = probability of success for a single trial Example 1 - a) Jason is rolling a die. Calculate the probability of getting a 1 on the 5th roll.~ b) What is the expected number of rolls before a 1 comes out?~ Example 2 A top NHL hockey player scores 93% of his shots in a shooting competition.~ a) What is the probability that the player will not miss the goal until his 20th try?- Note: Since the question is asking that the player does not miss the goal UNTIL his 20th try, this means he will miss on the 20th try. Therefore, the question is asking the probability of the NHL player missing on his 20th shot. So, the player's percentage of scoring is actually probability of failure.~ K Note: Because the player misses the 20th shot, it means he scored 19 of his previous shots. Since the scoring of the player is measured as unsuccessful, the number of unsuccessful trials iseb) What is the expected number of shots before he misses?~ c) What is the probability that the player will score 19 goals out of 20? - Note the difference between c and o - one is geometric and one is binomial!e