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difference between mutually exclusive events and independent events
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☼ Give the difference between mutually exclusive events and independent events.
| mutually exclusive events | Independent events | ||
| 1. | If the events are associated with the same experiments and their intersection is |
1. | If the events are associated with the different experiments then they are called independent events. |
| 2. | In tossing a die, if A is an event that getting 2, 4, 6 and B is an event that getting 3, 5. Then A |
2. | In tossing a die, if A is an event that getting 2, 4, and 6. While in tossing a coin, if B is an event that getting head (H). Then A and B are independent events. |
| 3. | If A and B are mutually exclusive events then P(A |
3. | If A and B are independent events then P(A |
e.g. (i) Let us consider the simultaneous throw of two coins.
Then, S = { HH, HT, TH, TT }
Let E1 = Event of getting at least one tail = { HT, TH, TT }.
E2 = Event of getting exactly two heads = { HH }.
Clearly, E1 E2 =
. So, E1 & E2 are mutually exclusive.
(ii) In simultaneous throw of two coins,
Let E1 = Event of getting head on first coin and E2 = Event of getting head on second coin. Then, E1 and E2 are independent events.
