Question 1125025
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There are five possible changes in her weight over the four days:
(1) gain all four days: 4(+2) = +8
(2) gain 3 of 4 days: 3(+2)+1(-1) = +5
(3) gain 2 of 4 days: 2(+2)+2(-1) = +2
(4) gain 1 of 4 days: 1(+2)+3(-1) = -1
(5) gain 0 of 4 days: 4(-1) = -4<br>
From this, we can see that the answer to the second question is 0 -- there is no possibility that her change in weight over four days is equal to +1.<br>
We also see that to lose one pound over the 4 days, she needs to gain 1 day and lose 3 days.  There are 4 ways she can do that -- do the weight gain on any one of the 4 days.<br>
There are 2 ways her weight can go each day; so over 4 days the number of different sequences of weight gains or losses is 2*2*2*2 = 2^4 = 16.<br>
So the probability of losing 1 pound over the 4 days is 4/16 = 1/4.