For three fair six-sided dice, the possible sum of the faces rolled can be any digit from 3 to 18.
For instance the minimum sum occurs when all three dices shows 1 (i.e. 1 + 1 + 1 = 3) and the maximum sum occurs when all three dces shows 6 (i.e. 6 + 6 + 6 = 18).
Thus, there are 16 possible sums when three six-sided dice are rolled.
Therefore, from the pigeonhole principle, <span>the minimum number of times you must throw three fair six-sided dice to ensure that the same sum is rolled twice is 16 + 1 = 17 times.
The pigeonhole principle states that </span><span>if n items are put into m containers, with n > m > 0, then at least one container must contain more than one item.
That is for our case, given that there are 16 possible sums when three six-sided dice is rolled, for there to be two same sums, the number of sums will be greater than 16 and the minimum number greater than 16 is 17.
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Answer:
The answer to m<v is 124°
Answer:
x=-9, x=4, x=-1/6
Step-by-step explanation:
Set the parentheses to zero to get your zeros.
Answer: 0.0084
Step-by-step explanation:
Let p be the population proportion of the creatures in Wonderland are anthropomorphic animals.
As per given, p = 0.70
Sample size : n=120
Let
be the sample proportion of the creatures are anthropomorphic animals.
Now, required probability :
![P(\hat{p}>0.80)=P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}>\dfrac{0.80-0.70}{\sqrt{\dfrac{0.70\times (1-0.70)}{120}}})\\\\P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}>\dfrac{0.10}{\sqrt{\dfrac{0.70\times 30}{120}}})\\\\ =P(Z>\dfrac{0.10}{\sqrt{0.00175}})\ \ \ \ \ [Z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}]\\\\ =P(Z>\dfrac{0.10}{0.04183})\\\\\=P(Z>2.39)\\\\=1-P(Z\leq2.39)\\\\=1- 0.9916= 0.0084](https://tex.z-dn.net/?f=P%28%5Chat%7Bp%7D%3E0.80%29%3DP%28%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%3E%5Cdfrac%7B0.80-0.70%7D%7B%5Csqrt%7B%5Cdfrac%7B0.70%5Ctimes%20%281-0.70%29%7D%7B120%7D%7D%7D%29%5C%5C%5C%5CP%28%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%3E%5Cdfrac%7B0.10%7D%7B%5Csqrt%7B%5Cdfrac%7B0.70%5Ctimes%2030%7D%7B120%7D%7D%7D%29%5C%5C%5C%5C%20%3DP%28Z%3E%5Cdfrac%7B0.10%7D%7B%5Csqrt%7B0.00175%7D%7D%29%5C%20%5C%20%5C%20%5C%20%5C%20%5BZ%3D%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%5D%5C%5C%5C%5C%20%3DP%28Z%3E%5Cdfrac%7B0.10%7D%7B0.04183%7D%29%5C%5C%5C%5C%5C%3DP%28Z%3E2.39%29%5C%5C%5C%5C%3D1-P%28Z%5Cleq2.39%29%5C%5C%5C%5C%3D1-%200.9916%3D%200.0084)
Hence, the probability that more than 80% of the sampled inhabitants are animals= 0.0084