Math511Exam1Solutions

A a darts player hits the bulls eye 70 of the time

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Unformatted text preview: P ( X | R ) = = = = = = P ( R) P ( R) 0.36 0.36 36 3 6. (a). A 20- sided die is rolled 80 times. What is the probability that it never shows a number above 17 (i.e., it never shows 18, 19, or 20)? Express your answer exactly and also as an approximation involving the number e. 4 20 4 ⎡⎛ 3⎞ ⎤ ⎛ 1⎞ 1 = ⎢⎜ 1 − ⎟ ⎥ ≈ ⎜ 3 ⎟ = 12 ⎝ 20 ⎠ ⎦ ⎝ e ⎠ e ⎣ n a⎞ ⎛ We used here the fact that lim ⎜ 1 + ⎟ = ea n→∞ ⎝ n⎠ (b). A box contains three cards with the number 8 on them, four cards with the number 9 on th...
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This note was uploaded on 01/25/2014 for the course MATH 511 taught by Professor Sumner during the Spring '13 term at South Carolina.

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