According to the Washington, D.C. Lottery’s website for its Cherry Blossom Double instant scratch game, the chance of winning a
prize on a given ticket is about 17%. Imagine that a person stops at a conveniencestore on the wayhome from work every Monday, Tuesday, and Wednesday to buy a scratcher ticket and plays the game. What is the probability that the player will not win on Monday or Tuesday, but will win on Wednesday?
the probability that the player will not win on Monday or Tuesday, but will win on Wednesday is the same as the probability of winning on the third trial.
This is an example of a geometric probability distribution because trials are repeated until the first success is gotten. Since chance of winning a prize on a given ticket is about 17%, it means that the probability of success, p = 17/100 = 0.17.
Let x represent the number of days before the person wins. The probability that it takes three days before the player wins is expressed as
