Answer:
8 hours
Steps:
Train 1:
Hours: 1, 2, 3, 4, 5, 6, 7, 8
Miles: 75, 150, 225, 300, 375, 450, 525, 600
Train 2:
Hours: 1, 2, 3, 4, 5, 6, 7, 8
Miles: 0, 0, 100, 200, 300, 400, 500, 600
To check all the events (6), we label the chips. Suppose one chip with 1 is labeled R1 and the other B1 (as if they were red and blue). Now, lets take all combinations; for the first chip, we have 4 choices and for the 2nd chip we have 3 remaining choices. Thus there are 12 combinations. Since we dont care about the order, there are only 6 combinations since for example R1, 3 is the same as 3, R1 for us.
The combinations are: (R1, B1), (R1, 3), (R1, 5), (B1, 3), (B1, 5), (3,5)
We have that in 1 out of the 6 events, Miguel wins 2$ and in five out of the 6 events, he loses one. The expected value of this bet is: 1/6*2+5/6*(-1)=-3/6=-0.5$. In general, the expected value of the bet is the sum of taking the probabilities of the outcome multiplied by the outcome; here, there is a 1/6 probability of getting the same 2 chips and so on. On average, Miguel loses half a dollar every time he plays.
Answer:
$12/25 pencils= $0.48 per pencil
Write this story as equations:
s = 5j
(s+12) = 2*(j+12)
Then solve:
5j+12 = 2j + 24 => 3j = 12 => j=4, s=5*4=20
Steve is 20, Janis is 4
In 12 years they will be 32 and 16
