Probability of Winning Arkansas Lottery Game

Question

From the e-Activity, determine the probability of winning your state’s (Arkansas) lottery game.  Provide a rationale to support your determination. 

Sample paper

Probability of Winning Arkansas Lottery Game

In one of the Arkansas Natural State Jackpot, the players are given a set of variables, 1 to 39, from which they choose 5 random variables of their choice. If all the 5 variables match those chosen by the Natural State Jackpot moderators, then the individual scoops the jackpot prize. There are also prizes for four and three matches, albeit smaller. To determine the probability of winning the lottery game, it is important to establish the total number of ways individuals can pick the lottery numbers. Now, the number of ways an individual can pick r items from a set of n items is given by (). r represents the five winning numbers, and n the total set of numbers.

The number of ways of picking 5 numbers from a set of 39 numbers is = 575,757

As such, the probability of winning the jackpot is

The probability of matching 4 out of the 5 winning numbers is as follows:

There are 5 winning tickets, of which, 4 tickets can win. The individual must select 4 of winning numbers, and 1 of the 34 non-winning numbers. The probability is thus given by:

= ( = 0.0002953

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