Probability Calculator

Probability Calculator

Use this calculator to find probabilities for single or combined events.

Select Probability Type: Single Event Probability (P(A)) Two Independent Events (P(A) × P(B)) Two Dependent Events (P(A) × P(B|A)) At Least One Event (1 – P(A’) × P(B’))

Calculate

Result:

Enter values and click Calculate.

🔹 Steps Used in Calculation

This calculator supports four types of probability calculations:

1. Single Event Probability

• Formula: P(A)P(A)P(A)
• The user enters the probability of a single event occurring.

2. Probability of Two Independent Events

• Formula: P(A∩B)=P(A)×P(B)P(A \cap B) = P(A) \times P(B)P(A∩B)=P(A)×P(B)
• This applies when the two events do not affect each other.
• Example: Probability of rolling a 6 on a die AND flipping heads on a coin:
  P(6)=16,P(H)=12P(6) = \frac{1}{6}, P(H) = \frac{1}{2}P(6)=61​,P(H)=21​
  P(A∩B)=16×12=0.0833P(A \cap B) = \frac{1}{6} \times \frac{1}{2} = 0.0833P(A∩B)=61​×21​=0.0833

3. Probability of Two Dependent Events

• Formula: P(A∩B)=P(A)×P(B∣A)P(A \cap B) = P(A) \times P(B|A)P(A∩B)=P(A)×P(B∣A)
• Used when one event influences the probability of the other.
• Example: Drawing two aces from a deck:
  P(A)=452P(A) = \frac{4}{52}P(A)=524​, P(B∣A)=351P(B|A) = \frac{3}{51}P(B∣A)=513​
  P(A∩B)=452×351=0.0045P(A \cap B) = \frac{4}{52} \times \frac{3}{51} = 0.0045P(A∩B)=524​×513​=0.0045

4. Probability of At Least One Event Occurring

• Formula: P(At Least One)=1−P(A′)×P(B′)P(\text{At Least One}) = 1 - P(A') \times P(B')P(At Least One)=1−P(A′)×P(B′) where P(A′)=1−P(A)P(A') = 1 - P(A)P(A′)=1−P(A) and P(B′)=1−P(B)P(B') = 1 - P(B)P(B′)=1−P(B).
• Used when calculating the probability of at least one of two events occurring.
• Example: Probability of getting at least one heads when flipping two coins: P(H)=0.5P(H) = 0.5P(H)=0.5, so P(T)=1−0.5=0.5P(T) = 1 - 0.5 = 0.5P(T)=1−0.5=0.5.
  P(At Least One)=1−(0.5×0.5)=0.75P(\text{At Least One}) = 1 - (0.5 \times 0.5) = 0.75P(At Least One)=1−(0.5×0.5)=0.75.

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🔹 Detailed Description

This probability calculator is useful for everyday situations, such as:

• Predicting Weather Events (e.g., the probability of rain in two different cities)
• Gambling & Games (e.g., dice rolls, card draws)
• Business Decisions (e.g., probability of customers making a purchase)
• Medical Risks (e.g., probability of a patient having two different conditions)

By selecting the appropriate probability type, you can quickly compute the likelihood of various outcomes.