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Probability Distribution of Rolling Two Dice

Calculate the probability distribution for the sum of two rolled dice, with values ranging from 2 to 12. Determine the most likely sum and the probability of specific outcomes.

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Probability Distribution of Rolling Two Dice

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  1. SOLUTION The possible values of X are the integers from 2 to 12. The table shows how many outcomes of rolling two dice produce each value of X. Divide the number of outcomes for Xby 36 to find P(X). EXAMPLE 1 Construct a probability distribution Let Xbe a random variable that represents the sum when two six-sided dice are rolled. Make a table and a histogram showing the probability distribution for X.

  2. EXAMPLE 1 Construct a probability distribution

  3. Use the probability distribution in Example 1 to answer each question. What is the most likely sum when rolling two six-sided dice? What is the probability that the sum of the two dice is at least 10? SOLUTION The most likely sum when rolling two six-sided dice is the value of X for which P(X) is greatest. This probability is greatest for X = 7. So, the most likely sum when rolling the two dice is 7. EXAMPLE 2 Interpret a probability distribution

  4. The probability that the sum of the two dice is at least 10 is: = P(X = 10) + P(X = 11) + P(X = 12) P(X > 10 ) 3 1 2 = + + 36 36 36 6 = 36 1 = 6 0.167 EXAMPLE 2 Interpret a probability distribution

  5. Make a table and a histogram showing the probability distribution for X. for Examples 1 and 2 GUIDED PRACTICE A tetrahedral die has four sides numbered 1 through 4. Let Xbe a random variable that represents the sum when two such dice are rolled.

  6. 3 16 What is the most likely sum when rolling the two dice? What is the probability that the sum of the two dice is at most 3? ANSWER sum of 5; for Examples 1 and 2 GUIDED PRACTICE A tetrahedral die has four sides numbered 1 through 4. Let Xbe a random variable that represents the sum when two such dice are rolled.

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