Mutually Exclusive And Independent Events Math

Probability of any event number of favorable outcomes total number of outcomes for mutually exclusive events p a or b which can also be written as p a b.

Mutually exclusive and independent events math. When tossing a fair coin twice the result of the first toss doesn t affect the probability of the outcome of the second toss and vice versa. Here are two events that are mutually exclusive. This means that a and b do not share any outcomes and p a and b 0. How to identify mutually exclusive events.

P a and b 0 the probability of a and b together equals 0 impossible. Therefore events a and b are mutually exclusive. Events are mutually exclusive events or disjoint if occurrence of one event excludes the occurrence of the other s. Mutually exclusive events are represented mathematically as p a and b 0 while independent events are represented as p a and b p a p b.

A and b are mutually exclusive events if they cannot occur at the same time. In a venn diagram the sets do not overlap each other in the case of mutually exclusive events while if we talk about independent events the sets overlap. When two events call them a and b are mutually exclusive it is impossible for them to happen together. Two events are independent if the outcome of one doesn t affect the outcome of the other.

Otherwise they are dependent. B the roll of a die is even. A the roll of a die is odd. Formulas of mutually exclusive events and independent events.

Clearly the roll of a die must result in a number that is either odd or even. The probability of a does not depend on whether b happens because it is 1 and similarly the probability of b does not depend on whether a happens because it is 0. It can t be both. For example suppose the sample space s 1 2 3 4 5 6 7 8 9 10.

Mutually exclusive events after learning about dependent and independent events it s time to mention mutually exclusive events. Probability independent and mutually exclusive events. If you have two events and a always happens and b never does or the reverse they are mutually exclusive because you never have both happen together. Both can t happen at the same time therefore their intersection is empty.