What are mutually exclusive events?

Two events are mutually exclusive if they cannot both occur at the same time. For example, getting heads and tails in a single coin flip. For mutually exclusive events, P(A and B) = 0, and P(A or B) = P(A) + P(B).

Probability Calculator – Simple, Addition & Multiplication Rule

Q: What is the basic probability formula?

P(E) = Number of favorable outcomes / Total number of outcomes. Probability always lies between 0 and 1. P(E) = 0 means impossible; P(E) = 1 means certain.

Q: What is the addition rule of probability?

P(A or B) = P(A) + P(B) - P(A and B). For mutually exclusive events (cannot happen together), P(A and B) = 0, so P(A or B) = P(A) + P(B).

Q: What is the multiplication rule of probability?

For independent events: P(A and B) = P(A) × P(B). For dependent events: P(A and B) = P(A) × P(B|A), where P(B|A) is the conditional probability of B given A.

Q: What is complementary probability?

The complement of event E is the event that E does NOT occur. P(not E) = 1 - P(E). For example, if P(rain) = 0.3, then P(no rain) = 0.7.

P(E) = Favorable outcomes ÷ Total outcomes. Also finds complementary probability P(Ē).

Favorable outcomes (m)

Total outcomes (n)

Enter valid non-negative integers. Favorable outcomes must be ≤ total outcomes.

P(A∪B) = P(A) + P(B) − P(A∩B). Enter 0 for P(A∩B) if events are mutually exclusive.

P(A)

P(B)

P(A∩B)

All values must be between 0 and 1. P(A∩B) must be ≤ min(P(A), P(B)) and P(A∪B) must be ≤ 1.

For independent events: P(A∩B) = P(A) × P(B). For dependent events, enter P(B|A) — the probability of B given A.

P(A)

P(B) — independent

Dependent events (enter P(B|A) instead of P(B))

P(A) and P(B) must be between 0 and 1.

How to Use

Choose the Rule

Select Simple for basic P(E), Addition Rule for P(A or B), or Multiplication Rule for P(A and B).

Enter Values

For Simple: enter favorable and total outcomes. For combined events: enter probabilities as decimals (e.g. 0.4 for 40%).

Get the Result

See the probability as a fraction, decimal, and percentage — with a complete step-by-step solution.

Frequently Asked Questions

What is the basic probability formula?

P(E) = Number of favorable outcomes / Total number of possible outcomes. Probability always lies between 0 and 1 inclusive. P(E) = 0 means the event is impossible; P(E) = 1 means it is certain.

What is the addition rule of probability?

P(A∪B) = P(A) + P(B) − P(A∩B). The subtraction removes the overlap counted twice. For mutually exclusive events (cannot happen together), P(A∩B) = 0, so P(A∪B) = P(A) + P(B).

What is the multiplication rule of probability?

Independent events: P(A∩B) = P(A) × P(B). One event does not affect the other.

Dependent events: P(A∩B) = P(A) × P(B|A), where P(B|A) is the conditional probability of B given that A has occurred.

What is complementary probability?

P(Ē) = 1 − P(E). The complement is the probability of the event NOT occurring. Example: if P(getting a 6 on a die) = 1/6, then P(not getting a 6) = 5/6. This is useful when P(not E) is easier to compute than P(E) directly.

What are mutually exclusive vs independent events?

Mutually exclusive: Events cannot occur simultaneously. P(A∩B) = 0. Example: getting H and T in a single coin flip.

Independent: Occurrence of one does not affect the other. P(A∩B) = P(A) × P(B). Example: flipping a coin twice — each flip is independent.

Note: mutually exclusive events with non-zero probability are always dependent (if A occurs, B cannot).

How is probability used in competitive exams?

Probability appears in SSC CGL, CHSL, IBPS PO, and Railway exams. Common problems involve: drawing cards from a deck (52 cards), rolling dice, drawing balls from a bag, coin tosses, and arrangements. Always identify the sample space (total outcomes) and favorable outcomes first.

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