No, two events are independent if the outcome of one does not affect the outcome of the other. They may or may not have the same probability.
Flipping two coins, or rolling two dice, are independent.
Drawing two cards, however, are dependent, because the removal of the first card affects the possible outcomes (probability) of the second card.
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No, the combined probability is the product of the probability of their separate occurrances.
It depends on whether or not the events are independent.
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The probability of winning two games with the same probability of 0.8 can be calculated by multiplying the probability of winning the first game (0.8) by the probability of winning the second game (0.8). Therefore, the probability is 0.8 * 0.8 = 0.64, or 64%.
Two events are said to be independent if the outcome of one event does not affect the outcome of the other. Their probabilities are independent probabilities. If the events are not independent then they are dependent.