Probability Calculator

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probability calculator
Single Event Probability (n/N)Independent Events (A AND B)Independent Events (A OR B)Mutually Exclusive (A OR B)
Results:
function toggleInputs(){var type=document.getElementById('calc_type').value;if(type==='single'){document.getElementById('single_inputs').style.display='table';document.getElementById('multi_inputs').style.display='none';}else{document.getElementById('single_inputs').style.display='none';document.getElementById('multi_inputs').style.display='table';}}function resetForm(){document.getElementById('calculatorAnswer').style.display='none';toggleInputs();}function calculateProbability(){var type=document.getElementById('calc_type').value;var showSteps=document.getElementById('steps').checked;var ansDiv=document.getElementById('answer');var container=document.getElementById('calculatorAnswer');var resultText=";if(type==='single'){var n=parseFloat(document.getElementById('fav_outcomes').value);var N=parseFloat(document.getElementById('total_outcomes').value);if(isNaN(n)||isNaN(N)||N<=0){alert('Please enter valid positive numbers');return;}var p=n/N;resultText='Probability P(E): '+p.toFixed(4)+'
Percentage: '+(p*100).toFixed(2)+'%
Odds: '+n+' : '+(N-n);if(showSteps){resultText+='
Step: P(E) = n/N = '+n+'/'+N+' = '+p.toFixed(4)+'
';}}else{var pa=parseFloat(document.getElementById('prob_a').value);var pb=parseFloat(document.getElementById('prob_b').value);if(isNaN(pa)||isNaN(pb)||pa1||pb1){alert('Please enter probabilities between 0 and 1′);return;}var finalP=0;var label=";if(type==='and'){finalP=pa*pb;label='Probability P(A \u2229 B)';if(showSteps)resultText+='
Step: P(A) \u00D7 P(B) = '+pa+' \u00D7 '+pb+'
';}else if(type==='or'){finalP=pa+pb-(pa*pb);label='Probability P(A \u222A B)';if(showSteps)resultText+='
Step: P(A) + P(B) – P(A \u2229 B) = '+pa+' + '+pb+' – ('+pa*pb+')
';}else if(type==='exclusive'){finalP=pa+pb;if(finalP>1){alert('The sum of mutually exclusive probabilities cannot exceed 1.');return;}label='Probability P(A or B)';if(showSteps)resultText+='
Step: P(A) + P(B) = '+pa+' + '+pb+'
';}resultText=''+label+': '+finalP.toFixed(4)+'
Percentage: '+(finalP*100).toFixed(2)+'%'+resultText;}ansDiv.innerHTML=resultText;container.style.display='block';}

Calculator Use

The probability calculator is a versatile tool designed to help you determine the likelihood of various events occurring. Whether you are dealing with a single dice roll, multiple independent events, or mutually exclusive scenarios, this calculator provides quick, accurate results in decimal, percentage, and ratio formats.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. By using this tool, you can visualize the statistical chance of outcomes in real-world scenarios, from insurance risk assessment to simple games of chance.

Favorable Outcomes (n)
The number of specific outcomes you are looking for (e.g., getting a "4" on a six-sided die is 1 favorable outcome).
Total Outcomes (N)
The total number of possible results in the sample space (e.g., 6 possible faces on a die).
Probability of Event A/B
A numerical value between 0 and 1 representing the likelihood of a specific event happening, where 0 is impossible and 1 is certain.

How It Works

To calculate the basic probability of a single event, the formula is the ratio of favorable outcomes to the total number of outcomes in the sample space. The general mathematical expression is:

P(E) = n(E) / n(S)

  • P(E): Probability of the event occurring.
  • n(E): Number of ways the event can occur.
  • n(S): Total number of possible outcomes in the sample space.

For more complex scenarios involving two events (A and B), the calculation depends on their relationship:

  • Independent Events (AND): P(A \u2229 B) = P(A) \u00D7 P(B)
  • Independent Events (OR): P(A \u222A B) = P(A) + P(B) – P(A \u2229 B)
  • Mutually Exclusive (OR): P(A \u222A B) = P(A) + P(B)

Calculation Examples

Example 1: Rolling a Die. What is the probability of rolling a 5 or a 6 on a standard six-sided die?

Step-by-step solution:

  1. Number of Favorable Outcomes (5 or 6) = 2
  2. Total Outcomes (1, 2, 3, 4, 5, 6) = 6
  3. Calculate: P = 2 / 6
  4. Result = 0.3333 (or 33.33%)

Example 2: Two Coin Flips. What is the probability of flipping "Heads" twice in a row (Independent AND)?

  1. P(Event A – Heads) = 0.5
  2. P(Event B – Heads) = 0.5
  3. Calculate: 0.5 \u00D7 0.5
  4. Result = 0.25 (or 25%)

Common Questions

What is the difference between probability and odds?

Probability is the ratio of favorable outcomes to the total number of outcomes. Odds, however, is the ratio of favorable outcomes to unfavorable outcomes. For example, if you have a 1 in 4 chance of winning, your probability is 0.25, but your odds are 1:3.

What are independent events?

Events are independent if the occurrence of one event does not affect the probability of the other event occurring. A classic example is flipping a coin twice; the first flip has no impact on the outcome of the second flip.

Can a probability be greater than 1?

No. By definition, probability ranges from 0 (impossible) to 1 (certainty). If your calculation results in a number higher than 1 or lower than 0, there is an error in the logic or the variables provided.

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