Question 1125025: Every day, Quinn either gains two pounds (with probability 1/2) or loses one pound (with probability 1/2). Each day these probabilities are independent of whether she lost or gained weight any other day.
At the end of four days, what's the probability that Quinn will weigh one pound less than she did before?
At the end of four days, what's the probability that Quinn will weigh one pound more than she did before?
Enter your answers as whole numbers or fractions in lowest terms.
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
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
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.
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.
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.
So the probability of losing 1 pound over the 4 days is 4/16 = 1/4.
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