Question:
Morgan is playing a board game that requires three standard dice to be thrown at one time. Each die has six sides, with one of the numbers 1 through 6 on each side. She has one throw of the dice left, and she needs a 17 to win the game. What is the probability that Morgan wins the game (order matters)?
Answer:
1/72
Step-by-step explanation:
<em>Morgan can roll a 17 in 3 different ways. The first way is if the first die comes up 5, the second die comes up 6, and the third die comes up 6. The second way is if the first die comes up 6, the second die comes up 5, and the third die comes up 6. The third way is if the first die comes up 6, the second die comes up 6, and the third die comes up 5. For each way, the probability of it occurring is 1/6 x 1/6 x 1/6 = 1/216. Therefore, since there are 3 different ways to roll a 17, the probability that Morgan rolls a 17 and wins the game is 1/216 + 1/216 + 1/216 = 3/216 = 1/72</em>
<em>I had this same question on my test!</em>
<em>Hope this helped! Good Luck! ~LILZ</em>
For 3. he answer is a
for 4 the answer is two
Answer:
And we can solve this using the following z score formula:
And if we use this formula we got:
So we can find this probability equivalently like this:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where 
and 
We select n =100. Since the distribution for X is normal then we know that the distribution for the sample mean 
is given by:
We want this probability:
And we can solve this using the following z score formula:
And if we use this formula we got:
So we can find this probability equivalently like this:
17x +x to the second power
6w-10 represents the total amount of fence will need to complete the rectangle of fence in his yard. The fence will need two lengths and 2 widths to complete the rectangle. If the width is w, and the length is 2w-5, then the total for the rectangle would be w+w+2w-5+2w-5 which simplifies to 6w-10.
