WEBVTT
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Two fair dice are rolled.
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What is the probability that the sum of the numbers rolled is eight?
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Any fair die has six faces numbered from one to six.
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We want the sum or total of our two numbers to equal eight.
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One way of answering this question is to set up a two-way table.
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Each of the two die could land on any number from one to six.
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For example, they could both land on one.
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This would give a sum or total of two.
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If the first die landed on one and the second die on two, we would have a sum of three.
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We can complete the table showing all the possibilities as shown.
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The probability of any event occurring can be written as a fraction, the number of successful outcomes over the number of possible outcomes.
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In this question, a successful outcome would be a sum of eight.
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There are five ways this could occur: rolling a two and a six, a three and a five, two fours, a five and a three, and a six and a two.
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This means the number of successful outcomes is five.
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There are 36 possible outcomes as there are 36 numbers in the table; six multiplied by six is 36.
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When two fair dice are rolled, the probability that the sum of the numbers is eight is five out of 36.
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An alternative method here would be to list the successful outcomes or combinations: two and six, three and five, four and four, five and three, and six and two.
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As there are five of these, we know that the correct probability is five out of 36.