What is Probability

In math, probability is the study of the likelihood of an event occurring. If you flip a coin, what is the probability that the coin will land on heads? Probability of this event occurring is expressed either as a fraction or a decimal from 0 to 1. If the event is unlikely to happen, then the probability will be closer to 0. If the event will likely happen then the probability will be closer to 1.

Probability will take into account all the ways that the event can happen. Since there are two sides of the coin: heads and tails, in one event (1 toss), the coin has one head side yet there are 2 sides of the coin. Thus, the probability of heads being flipped during one toss is 1/2 or .5 (50%). Dependent on how many coin tosses take place, you can figure out the likelihood of the coin landing on heads after a set number of tosses and the fact that the coin can land on tails. In this case, the probability of heads or tails is independent or not affected by the previous flip. Because of this, then you know that every toss can have two outcomes. Thus, if you perform 7 coin tosses then what is the probability of you landing heads all 7 times? Since there are two outcomes, then out of 7 tosses, there will be 2*2*2*2*2*2*2= 128 outcomes. Because one side out of two is heads, the probability of landing all heads for the 7 tosses is (1/2)*(1/2)*(1/2)*(1/2)*(1/2)*(1/2)*(1/2)=1/128 or .01.

Probability can be dependent on the outcome of prior events, which means that the future outcome is affected by a previous outcome. For example, what is the probability that 3 jacks will be drawn in a row from a 52 card deck? Since there are 4 jacks in a 52 card deck, then the first pick defines that there are 4 chances out of 52 cards (4/52). Now that one jack has been picked then there are only 3 jacks remaining out of 51 cards (3/51). The last draw will then be 2 remaining jacks out of 50 remaining cards (2/50). Thus, the probability of 3 jacks being drawn in a row from a 52 card deck is (4/52)*(3/51)*(2/50)=24/132600=1/5525.

Once you determine if the outcomes are dependent or independent, the solution finds all the possible combinations in which the event may occur. Therefore, you can understand that probability is a logical math concept that has practical applications. Many of the applications has grown in the area of finances, risk management, and product reliability. So what is the likelihood that you will apply probability in the next five years?