Dave is taking a algebra ii test and comes across this question: you have two die that you will roll. you will sum up the face v
alues and record the sum in a chart. you need to complete 250 trials and find the probability of rolling a sum of 8. unfortunately, he does not have enough time to complete all 250 trials so he is going to make an educated guess. what is his guess and how did he use the law of large numbers to help him
Answer: B.) Dave guessed 0.14. The law of large numbers states that as the number of trials increases the experimental probability approaches the theoretical probability. He determined the theoretical probability would be
5
36
. With 250 trials he could use the law of large numbers and expect the experimental probability to be near there.
When you are rolling two dice there are 36 probabilities. In order to get an 8, there are 5 possibilities.
2 + 6, 3 + 5, 4 + 4, 5, + 3, 6 + 2
Therefore, the chances of an 8 are 5/36. Multiplying this by 250 gives us about 34.
The law of large numbers helps because it says the more rolls that take place, the more likely we are to get close to the expected value. With 250 rolls we should get pretty close.
Jupiter's menagerie of moons includes the largest in the solar system (Ganymede), an ocean moon (Europa) and a volcanic moon (Io). Many of Jupiter's outer moons have highly elliptical orbits and orbit backwards (opposite to the spin of the planet).
