Let X denote the random variable that gives the sum of the faces that fall uppermost when two fair dice are rolled. Find P(X = 11). (Round your answer to two decimal places.)
To find the probability P(X = 11), we need to determine the number of favorable outcomes and the total number of possible outcomes.
When two fair dice are rolled, each die has six possible outcomes (numbers 1 to 6). The total number of possible outcomes is the product of the number of outcomes of each die, which is 6 * 6 = 36.
To find the favorable outcomes, we need to determine the pairs of numbers that sum to 11.
The possible pairs that sum to 11 are: (5, 6), (6, 5).
Therefore, the number of favorable outcomes is 2.
The probability P(X = 11) is the ratio of the number of favorable outcomes to the total number of possible outcomes: P(X = 11) = 2/36.
To round the answer to two decimal places, we divide 2 by 36 and round the result to two decimal places.