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The days in a certain month are classified as rainy days, hot days, both rainy and hot days, or neither rainy nor hot days.
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Let π
denote rainy days and let π» denote hot ones.
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Use the Venn diagram below to calculate the probability that a day is not rainy.
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The Venn diagram shown has two circles representing rainy and hot days.
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The number in the intersection of both circles represents days that were both rainy and hot.
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And the number outside the two circles represents the number of days that were neither rainy nor hot.
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In this question, we are asked to calculate the probability that a day is not rainy.
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Letβs begin by calculating the total number of days in the month.
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This is the sum of nine, four, two, and 15.
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As this is equal to 30, there are 30 days in the given month.
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The circle that represents rainy contains a four and a two.
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There were four days that were just rainy and two days that were rainy and hot.
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This gives a total of six rainy days.
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The probability that a day is rainy is therefore equal to six out of 30.
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Both the numerator and denominator here are divisible by six.
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This means that the fraction simplifies to one-fifth.
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And the probability that a day is rainy is one-fifth.
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We could work out the number of days that are not rainy by adding those numbers outside of the circle in the Venn diagram.
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Alternatively, we can use our knowledge of the complement of an event denoted π΄ bar or π΄ prime.
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The probability of π΄ bar is equal to one minus the probability of π΄.
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This means that the probability that a day is not rainy is one minus one-fifth, which is equal to four-fifths.
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This fraction is equivalent to 24 over 30, which is the number of days it did not rain over the total number of days.