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Let π denote a discrete random variable which can take the values negative two, two, four, and five.
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Given that the probability π equals negative two is 0.15, the probability π equals two is 0.43, and the probability π equals four is 0.25, find the probability π is greater than two.
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In this question, weβre not asked to determine the probability that our random variable is equal to a particular value, but rather the probability that it is greater than a given value.
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This may look a little confusing at first, but the key to remember is that a discrete random variable can only take the values in its range and no others.
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Letβs begin by representing information in the question using a table.
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We have the values in the range of our discrete random variable in the top row and the corresponding probabilities in the second row.
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Now, we do have a missing probability, the probability that π equals five, but weβll worry about that later if necessary.
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We want to find the probability that π is greater than two.
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Now remember that our discrete random variable can only take the values in its range.
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For π to be strictly greater than two, this means that it must either take the value four or the value five.
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There are no other values it can take.
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The probability π is greater than two then is equal to the sum of the probability π equals four and the probability π equals five.
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Now remember, we donβt know the probability π equals five, although we can easily calculate it by remembering that the sum of all probabilities in the distribution must be equal to one.
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Instead, a slightly easier way may be to recall that the probability π is greater than two will be equal to one minus the probability π is less than or equal to two.
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So, instead, we can just subtract the probabilities for π equaling negative two and π equaling two from one, one minus 0.15 and 0.43, which is equal to 0.42.