Electron Waves and Wave Functions solutions

Electron Waves and Wave Functions solutions - Physics...

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Physics 6 (2006) Homework 4 Solutions 1 a) Prob for one 5 in 1 st roll: (1/6) b) Prob for 5 followed by anything other than 5 is (1/6) × (5/6) AND Prob for not-5 followed by 5 is (5/6) × (1/6). So total Prob to get ONLY one 5 is sum of these two, or 2 × (1/6) × (5/6)=10/36=0.278 c) Prob for at least one 5 will be the same as part (b) with the addition of the Prob for two 5’s in two rolls. That latter is (1/6) 2 =1/36. The total is then 10/36 + 1/36 = 11/36 =0.306 d) In three rolls of the dice there can ONLY be 0 or 1 or 2 or 3 fives. There are no other possibilities. So the addition of each of the possibilities must add to 1.0 e) Prob of ONLY one 5 in eight rolls? To get a five on the 1 st roll and not the next 7 rolls is just Prob of (1/6) × (5/6) 7 . But there are seven other ways to get only one 5 in eight rolls. The final result will be 8 × (1/6) × (5/6) 7 = 0.372 f) There are many ways to have only two 5’s turn up in eight rolls. How many? 7 ways for the 2 nd 5 if the 1 st roll produces a 5 + 6 ways for the 3 rd or 4 th or … or 8 th
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