Next week’s forecast predicts that there is a 74-percent chance that it will rain, describe the complementary event and its probability.
The complementary of an event would be that the event would not happen. So our event was that it was going to rain, which means our complementary event would be that it will not rain. The probability of an event plus the probability of the complement of the event, so it not happening, should equal 100 percent or 1.0.
Therefore, the probability of it raining plus the probability of it not raining should be 100 percent. Therefore, we can replace the probability of it raining with 74 percent since it was given to us, and we can find the probability of it not raining by letting it be 𝑥 and solving for it.
So in order to solve for 𝑥, we need to subtract 74 percent from both sides of the equation. The 74 percents cancel on the left, and 100 percent minus 74 percent is equal to 26 percent. Therefore, there is a 26-percent chance that it will not rain.