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UHealth PATELLAR TENDU Secure https://www.mathxl.com/Student/PlayerHomework.aspx?home worklde440994463 Math 1300 FS2017 omework: Homework 11 core: 0 of 1 pt Gen Interest 7.4.19 22 of 30 (20 complete) Two dice are tossed and the larger of the numbers showing is recorded. Find the expected value of this experiment The expected value of this experiment is(Round to the nearest hundredth as needed.) Enter your answer in the answer box and then click Check Answer. All parts showing Clear All esc F7 FS F6Explanation / Answer
Sinec we are taking larger of the 2 numbers, there will be cases where both the numbers are the same. In such cases we take that number as the largest.
The sample space that 1 is the larger of the 2 numbers = 1 (1,1)
The sample space that 2 is the larger of the 2 numbers = 3 [(1,2), (2,2) and (2,1)]
The sample space that 3 is the larger of the 2 numbers = 5 [(1,3),(2,3) (3,3) (3,2)and (3,1)]
The sample space that 4 is the larger of the 2 numbers = 7 [(1,4),(2,4),(3,4) (4,4) (4,3), (4,2) and (4,1)]
The sample space that 5 is the larger of the 2 numbers = 9 [(1,5),(2,5),(3,5), (4,5),(5,5) (5,4), (5,3),(5,2) and (5,1)]
The sample space that 6 is the larger of the 2 numbers = 11 [(1,6),(2,6),(3,6), (4,6),(5,6) (6,6), (6,5),(6,4), (6,3), (6,2) and (6,1)]
The probability when throwing 2 dice is = 1/36 (as there are 36 samples)
Therefore Expected value = SUM [x * P(x)]
Expected value for 1 = 1 * 1/36 = 1/36
Expected value for 2 = 2 * 3/36 = 6/36
Expected value for 3 = 3 * 5/36 = 15/36
Expected value for 4 = 4 * 7/36 = 28/36
Expected value for 5 = 5 * 9/36 = 45/36
Expected value for 5 = 6 * 11/36 = 66/36
Therfore expected value = (1/36 + 6/36 + 15/36 + 28/36 + 45/36 + 66/36) = 161/36 = 4.47
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