- ! ; UF ESI 6321 Pre-Wark Assignment Due August 17, 2007 Luther Setzer 5- 7 i z zJ .>( :r L J 3 ) / / f ( t / " ( , . / l---' Pre- J.'~ P( I rf JJ:-, J o-rl J,"<"- o.J{ '1 ' +. j) .- ~0 I ~ ," . / ' { ' ( ( /-- . UF-ESI-632I 7/11/2007 2-1. A four-sided die is engraved with the numbers 1 through 4 on its four different sides. Suppose that when rolled, each side (and hence each number) has an equal probability of being the bottom face when it lands. We roll two such dice. Let X be the sum of the numbers on the bottom face of the two dice. (a) What is the probability that X is at least five? Listing the possible combinations of the two dice: I 1 12 13 14 2 I 22 23 24 3 I 32 33 34 41 42 43 44 This yields 16 possiblities. Ten have the sum of five or greater. Thus, 10116= 5/8 .,/* (b) How does your answer to (a) change if you are told that the bottom face of the first die has the number "3" on it? :, I J I I oJ' I' 1 . . . l ( If the bottom number is three then the first die that means the only combinations you can count are the ones that have 3 as the first number. 3/16 I fl' (c) How does your answer to (a) change if you are told that the bottom face ofone of the dice has the number "3" on it? This Would~be 3116 for the same reason as (b)~ ) Luther Setzer I NASA Pkwy EStop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435 ?(A Or ~) :- peA) + 1(6)- f(A~n~)JS) I f A ~ g (M< hM.\..f,..~ (X ~ . ~ v tl.) P( A r .:- f (A) .-t P( D) f CA a.l l)') : f CA) r (D I A) UF-ESI-632I 7/11/2007 page~ of 1 ~ 2-5. In Oblako County, any day can be either sunny or cloudy. If a day is sunny, the following day will be sunny with probability 0.60. If a day is cloudy, the following day will be cloudy with probability 0.70. Suppose it is cloudy on Monday. (a) What is the probability that it will be sunny on Wednesday? PTuesday _sunny= 0.30 PWednesday_sunny = 0.39 ~ ...- (b) What is the probability that it will be sunny on both Tuesday and Wednesday? Luther Setzer I NASA Pkwy EStop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435 .-- - _ D.b' 0 , \ / p r ( ( ~ r~ ... ( ~ ~ ) .., (,.,;J-"~ - .:l L \ \..' " '-' &-< ( = )J ~ . 7> ((~d a ,,) ~ ~ )-+ r (v",ii ~ S<.,< c..,.. J . ::.- l( r~~) 'P (SAA~ l.r~) -\- 7>( , 1 ) . r (yo.( I,...; 1) UF-ESI-632I 7/11/2007 2-7. It is a relatively rare event that a new television show becomes a long-term success. A new television show that is introduced during the regular season has a 10% chance of becoming a long-term success. Pregular_success:= 10% A new television show that is introduced as a mid-season replacement has only a 5% chance of becoming a long-term success. Approximately 60% of all new television shows are introduced during the regular season....
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