You take the number of possible 13 card hands with no 9 in them and subtract that from the total number of possible 13 card hands 9's included.
so C(52,13) - C(48,13) The number of all possible 13 card hands is: 52!/13!(52-13)! or 52!/13!*39! which is 635,013,559,600
The number of all possible 13 card hands with no 9s is:
48!/13!(48-13)! or 48!/13!*35! = 192,928,249,296
The difference is 635,013,559,600 - 192,928,249,296 = 442,085,310,304
So 442,085,310,304 out of 635,013,559,600 hands will have at least 1 nine. The ratio of 442,085,310,304 to 635,013,559,600 is 0.696182472... So roughly 70% of the time
27,630,331,894/39,688,347,475 is the best I could do for a whole number ratio.
The researchers proved that exercise causes weight loss only for high school students.
Step-by-step explanation:
We are told that the researchers found a high correlation, 0.93, between amount of exercise and weight lost.
Now, looking at each of the options;
- A is True because due to the high correlation, the research proves that exercise causes weight loss but only for high school students.
- B is not true because we are told the correlation is very high at 0.93. Thus, it is untrue that there is no proven causation.
-C is not true because there's no where that the researchers have completely proved that exercise causes weight loss generally. It is only peculiar to the high school students studied.
-D is not true because the 93% is just a correlation and not a percentage of those who lost weight
