Calculate probability for single events, multiple events (AND, OR), and binomial distributions. Convert between probability, percentage, and odds with step-by-step explanations.
Probability
0.1667
16.67%
P(A) = Favorable Outcomes / Total Outcomes
1 favorable outcomes out of 6 total possibilities.
P(A) = favorable / total
P(not A) = 1 - P(A)
P(A and B) = P(A) × P(B)
P(A or B) = P(A) + P(B) - P(A∩B)
Probability
0.1667
16.67%
Probability measures how likely an event is to occur, ranging from 0 (impossible) to 1 (certain). Basic formula: P(A) = favorable outcomes / total outcomes. For multiple independent events: P(A and B) = P(A) x P(B). For either event: P(A or B) = P(A) + P(B) - P(A and B). Odds represent the ratio of success to failure.
Probability is the mathematical study of chance and uncertainty. It measures the likelihood of an event occurring as a number between 0 and 1 (or 0% to 100%). Probability theory is fundamental to statistics, data science, gambling, insurance, weather forecasting, and scientific research involving uncertainty.
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Probability measures how likely an event is to occur, ranging from 0 (impossible) to 1 (certain). Basic formula: P(A) = favorable outcomes / total outcomes. For multiple independent events: P(A and B) = P(A) x P(B). For either event: P(A or B) = P(A) + P(B) - P(A and B). Odds represent the ratio of success to failure.
Probability measures the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). It's calculated as the number of favorable outcomes divided by the total number of possible outcomes. A probability of 0.5 means a 50% chance.
Independent events don't affect each other's probability (like coin flips). For independent events, P(A and B) = P(A) × P(B). Dependent events influence each other (like drawing cards without replacement). Dependent events require conditional probability.
The complement of event A is "not A" - all outcomes where A doesn't occur. P(not A) = 1 - P(A). If there's a 30% chance of rain, there's a 70% chance of no rain. Complements always sum to 1 (100%).
The binomial distribution models the probability of getting exactly k successes in n independent trials, each with probability p of success. Formula: P(X=k) = C(n,k) × p^k × (1-p)^(n-k). Example: probability of getting 3 heads in 5 coin flips.
For mutually exclusive events (can't both happen): P(A or B) = P(A) + P(B). For non-mutually exclusive events: P(A or B) = P(A) + P(B) - P(A and B). The subtraction avoids counting the overlap twice.
Probability is favorable/total outcomes. Odds compare favorable to unfavorable outcomes. If probability is 1/4 (25%), odds are 1:3 (1 favorable to 3 unfavorable). To convert: odds a:b means probability = a/(a+b).
Last updated: 2025-01-15
Probability
0.1667
16.67%