Probability, Sample Sets, Odds

Probability is a basic mathematical concept that requires one to understand how odds work. Probability is a useful skill to have, whether for playing cards, or for implementing things like decision trees in business, where ideas like compound probabilities come into play. This paper will examine a few basic probability questions in order to outline how probability works and how it can be applied.

The sample space is the set of all possible outcomes. Each possible outcome is an element. In this roll of the die there are 16 elements. Each of the first die rolls (1, 2, 3, 4) can be paired with one of the second die rolls (5, 6, 7, 8), to give a total of 16 possible combinations. Because of the nature of the dice, there is no overlap.

The event of two dice sum to 8 can have a few different outcomes, being any possible combination that adds to 8. With these two dice, the following possible combinations add to eight: {1,7}, (2,6}, (3, 5}. There is no zero die, so there are only three possible combinations that will sum to 8.

c. The event probability is the total number of possible events that sum to 8 divided by the total number in the sample space. Thus, 3 / 16 = 18.75%

Question #2

The odds of drawing three jacks are the odds of any one draw being a jack. This assumes no replacement of cards previously drawn, so that for the second draw there is one fewer jack and one fewer total cards. So the odds of the first draw being a jack are 4/52. The odds of the second draw being a jack are 3/51, and the odds of the third draw being a jack are 2/50. To find the cumulative odds, so the odds that all three events occur, they must be multiplied together:

These odds are therefore 0.0181%

Question #3