How to Find Probability

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How to Find Probability

Last updated on September 25th, 2020

Probability is the likelihood of one or more events happening divided by the number of possible outcomes. You can break down the problem into separate probabilities and multiple the separate likelihoods by one another to count the probability of multiple events. Here is how to calculate the probability of single and multiple random events and also converting odds to probability. 

\[Probability = {The\ number\ of\ wanted\ outcomes \over The\ number\ of\ possible\ outcomes}\].

How to Find the Probability of a Single Random Event

  1. Determine a single event with a single outcome.

    Example: The probability to get a 6 when you roll a die.

    A die has 6 sides, 1 side contains the number 6 that give us 1 wanted outcome. 

  2. Identify the total number of outcomes that can occur.

    There are six possible outcomes when you roll a die. 

  3. Divide the number of events by the number of possible outcomes.

    Probability = {The\ number\ of\ wanted\ outcomes \over The\ number\ of\ possible\ outcomes} = {1 \over 6}

  4. Add up all possible event likelihoods to make sure they equal 1.

    The likelihood of rolling a 6 on a 6-sided die is 1/6. But the probability of rolling all five other numbers on a die is also 1/6. 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 6/6 , which = 100%.

How to Find the Probability of a Multiple Random Events

There are four kinds of multiple random events and which are Independent Events, Dependent events, Exclusive events, and Inclusive events. 

Independent events: Two events are independent when the outcome of the first event does not influence the outcome of the second event. Multiply the probability of the first event by the probability of the second event is the probability of two independent events. 

P(X and Y) = P(X) P(Y)

Example: If one has three dice what is the probability of getting three 4s? 

  1. Determine each event you will calculate.

    The probability of getting a 4 on one die is 1/6

  2. Calculate the probability of each event.

    The probability of getting 3 4s is: 1/6, 1/6, 1/6